English Guide: Practical Tips for Better English Communication

thank you We all have certain people in our life to whom we are really thankful. It may be because they might have helped us or have been there when we needed their support.To show our courtesy, we must thank them in a good way. People give chocolates, gifts etc. to show the gratitude. The simplest form of expressing gratitude is by using the kind words. So, let us have a look at some of the best ways to thank someone. 8 Interesting ways to thank someone1....
sad baby In life, there are times when we feel low and upset. This situation comes when some unexpected things happen. We all, for sure, might have faced this kind of situation at least once in our lifetime. However, these things are very common and expressing them in English is not uncommon. In this blog, you will learn about some interesting slang words to express and describe disappointment.8 slang words to describe disappointment1. Bummer or Bummer...
Jam session In today’s competitive and busy world, it is not easy to get a job in an MNC company. As there are many candidates who apply on a daily basis, it becomes difficult for the HR to conduct the interviews. Hence, they conduct various rounds and the one who clears reaches the final round. These rounds include group discussions, written tests, and a JAM session. While you might be aware of tests and group discussions, JAM can be described as a short...
pronounce words English is the only language which is spoken widely all over the world as it can be easily learnt and understood. One of the old yet easiest way to learn English is by reading newspapers, books, novels etc. You might find range of vocabularies to learn. Pick up 10 new words and learn the meaning, spelling, pronunciation etc. Unfortunately, there are many words which are pronounced incorrectly. According to a recent research almost 82% of the...
travel idiom An idiom is an expression, word or a phrase that has a figurative meaning. They don’t mean exactly what the word say. They have hidden meaning. Like for example, “it’s raining cats and dogs”. The sentence doesn’t mean the way it is said or written. However, the sentence means it is raining heavily. In this blog, we will discuss travel idioms.Travel Idioms one must know1. Asleep at the wheel: Not attentiveExamples:Yash scored less marks in the final exams...
travel idiom In the previous blog, we explained some interesting travel idioms. In today’s blog, we will explain some more travel idioms that will help to improve English communication skills. Let us learn those travel idioms.8 Travel Idioms you must know1. Road rage: anger or violence towards other drivers.Examples:While returning from Pune, our driver had a road rage with the other driver.Earlier today a man was arrested for attacking a motorist in a...
phrasal verb with do Phrasal verbs are a combination of a verb and preposition, a verb, and an adverb. They are also known as ‘compound verb’. For e.g. - Don’t put me off, I am trying my best. There are many phrasal verbs which we use in our day to day communication. In today’s blog, we will explain phrasal verbs using the word “do”.Phrasal verbs using do:1. Do up: make something look good.Examples: I will help you to do up your hair.You should try doing up...
bossy   In the professional world, we use a formal English for communicating with our colleagues. But sometimes bosses and managers use expressions which you have never heard about. In today’s blog, we are bringing you bossy words which you need to understand in order to be comfortable and stable in the professional world.8 Bossy words you must know:1. Under my nose: to do some work under someone’s supervision.Examples: The new boss is so strict that every employee...
idiom world In your day to day life you meet many people with different behaviours and attitudes. Some are short-tempered, some are down to earth while some are shy and others are talkative. While maintaining friendship with them, you might have surely faced a situation where you had to stop someone from talking  rubbish things. Situations like these need to be handled calmly without actually offending the person. In this blog, we bring you idioms that can...
homophone Have you heard these words- ad, add; bare, bear; been, bean and got confused with the spellings? These words are pronounced in a similar way but are spelled differently and mean different. These words are known as homophones. There are some more examples of homophones. So, let us have a look at some more interesting homophones. 7 interesting homophones:1. Allowed and AloudAllowed means when you get a permission from someone to do...
socializing in English In our day to day life, we use many words to converse in English. Many of these words used are a combination of a verb and a preposition or a combination of verb and adverb. These words are called Phrasal verbs. These words give an entirely different meaning when combined. It is vital to know their proper meaning in order to use them in a sentence. Till now we have listed many blogs related to phrasal verbs and its usage to describe your day....
car All these years we published blogs that were related to interview skills or English grammar. Just a few days back we started creating more blogs that helped the beginners to learn basic English skills. The basic English skills include vocabularies, phrases, idioms that are used in day to day communication. While the blogs provided information on general topics, today’s blog is for those who love cars, bikes etc. i.e. for men and boys. However,...
funny idiom to improve English 1 In our last blog, we described funny idioms that are often used by the native speakers in the day to day communication. Funny idioms not only add a humorous touch but also make you a pro-English speaker. Let us have a look at the remaining idioms that are funnier than the previous one. 6 Funny idioms you must know1. Chew the fatThis idiom means to chat in a friendly and leisurely way or engage in casual gossip sessions. It is generally said to...
funny idiom to improve English Idioms are an everyday figure of speech which is taken in a light and a humorous way. The figurative meaning of the idioms makes the sentence often go against the logical “rules of language and grammar”.  Native speakers use these idioms daily in the conversation which not only improves English but also helps to get the command over the language. In today’s blog, we’ll teach funny idioms which will help improve your English-speaking skills.5...
confused In life, we have faced many instances where we have misunderstood many things and have ended up confused. We were able to clear a few, while there was a lot of confusion in the others. It is important to clarify and clear out the confusion in order to avoid unexpected results. To understand and clarify the confusion, you are required to articulate the points in an impeccable English with good vocabulary words. Today’s blog will help you with...
food “Food is love food is life” for all the food lovers. It’s hard to define the relation that the food lovers share with food. While people explore cuisines from different places to get a sense of taste, they also learn many new things. Learning new things is easy and so is English. As a foodie, you learn new dishes and its ingredients which indirectly help you to learn new words, spellings and pronunciation. Sometimes describing them is difficult as there...
food vocabulary In our last blog, we described vocabulary related to texture of the food. This blog will introduce more words about food that can be used while communicating. Food vocabulary is useful for everyone – right from the housewives to the food lovers. Have you ever been in the phase where you found it difficult to explain a recipe in English? If your answer is yes, then don’t worry. It’s something that everybody has gone through. There are many words that...
conversation starters When you go to a new place, where you don’t know anyone, it becomes a bit difficult to spend the time. In order to know more about the festival, culture, climate etc. of that place you decide to explore the city. You find a group of locals there and decide to make friendship and know about the city. A fluent English, in this case, is very helpful to start the conversation. You need to be aware of the conversation starters that will encourage...
grammar mistakes Are you a beginner in English? It is common to get confused with similar words or phrases. Speaking English is easy as it just takes confidence and a person to talk with. Don’t be afraid of mistakes, mistakes are the proof that you are trying. Only by making mistake you can learn new things. It is not that you are the only one who is making mistakes. There are many native English speakers who get confused while speaking. The mistakes can be...
teen slang Slang words are informal language words that are used by the teens and youngsters. Today, it’s impossible to be in a nightclub, or at a cutting-edge art gallery, without hearing these slang words. These are nothing but idioms and expressions, which make adults scratch their head. Don’t worry, this blog will explain you slang words along with its meaning.10 slang words you must know1. It sucks / that sucksMeaning - It might not be the right...
misused words literally In our last blog, we discussed words that are commonly misused in English. In this article, we will add some more words that are commonly misused. Knowing the correct usage will help you to enhance your vocabulary as well as spoken English Skills which will help you to speak effectively. Let us look at the words.10 words with incorrect usage1. An effectAn effect means either to influence or to fake whereas to effect means to put into effect.Examples:The new...
you can do it In life, there are many situations which make us sad and feel low. At that moment when someone encourages us with their positive words, we feel light and happy.  Don’t we? We encourage people playing sports, while building relationships with friends, family, colleagues, and while working. In the same manner, when your friend or your loved one feels low, you try to encourage them with positive words by complimenting and appreciating them. In...
give it a shot In our last blog, we taught you few phrases that can be used for encouraging someone. When you use these phrases in your communication, it not only helps you to motivate someone but also improves your English-speaking skills. Let’s have a look at some positive phrases that will improve your English skills and help you encourage someone.6 phrases you must know1. You are almost there!This phrase is best to encourage someone who is about to...
interjections In our earlier blog, we provided a fun guide to interjections which help us in our day to day conversation. Interjections are words for the emotions and expressions that we make. These interjections words depict our emotions like surprise, agreement, disagreement, sarcasm, shock etc. In today’s blog, we will explain interjections to be used to express your emotions which will help you in your everyday conversations using “expressive...
couch potato Idioms play an important role in English language. They help to express your feelings in a figurative manner. In today’s lesson, we will describe people and their characteristics with idiomatic expressions. These people might be your friends, cousins, co-workers and to some your family members. All these characters are different from each other and have a unique differentiating factor through which we identify or know them. Let us learn the...



An equation involving trigonometric ratios of an angle is said to be a trigonometric identity if it is satisfied for all values of that angle for which the given trigonometric ratios are defined. Trigonometric identities are equalities that involve trig_id_2trigonometric functions and are true for every single value of the occurring variables.

We have three main trigonometric identities:

•    Sin2 θ + Cos2 θ = 1

•    Sec2 θ = 1 + Tan2 θ

•    Cot2 θ + 1 = Cosec2 θ

Let’s discuss each of the above trigonometric identity in detail:

Sin2 θ + Cos2 θ = 1

In the adjoining figure, we have Δ ABC right angled at C.

trig_id_1According to Pythagoras theorem:

AB2 = AC2 + BC2 … (i)

Divide each term of above equation (i) by AB2

AB2 = AC2 + BC2    … (ii)
AB2     AB2     AB2

As we know, Sin θ = Opposite / Hypotenuse

Sin θ = BC / AB
And, Cos θ = Adjacent / Hypotenuse
Cos θ = AC / AB

Putting the values of Sin θ and Cos θ in equation (ii)

1 = Cos2 θ + Sin2 θ

This is true for all θ such that 0° ≤ θ ≤ 90°. So, this is a trigonometric identity.

Sec2 θ = 1 + Tan2 θ

In the adjoining figure, we have Δ ABC right angled at C.trig_id_1

According to Pythagoras theorem:

AB2 = AC2 + BC2 … (i)

To prove next identity we will divide equation (i) by AC2

AB2 = AC2 + BC2    … (iii)
AC2     AC2    AC2

As we know, Secant θ = Hypotenuse / Adjacent

Secant θ = AB / AC
And, Tangent θ = Opposite / Adjacent
Tangent θ = BC / AC

Putting the values of Secant θ (Sec θ) and Tangent θ (Tan θ) in equation (iii)

Sec2 θ = 1 + Tan2 θ

Tan θ and Sec θ are not defined for θ = 90°

So the above equation is true for all θ such that 0° ≤ θ < 90°

Cot2 θ + 1 = Cosec2 θ

In the adjoining figure, we have Δ ABC right angled at C.

trig_id_1According to Pythagoras theorem:

AB2 = AC2 + BC2 … (i)

Next we will divide equation (i) by BC2

AB2 = AC2 + BC2    … (iv)
BC2     BC2     BC2

As we know, Cotangent θ = Adjacent / Opposite

Cotangent θ = AC / BC
And, Cosecant θ = Hypotenuse / Opposite
Cosecant θ = AB / BC

Putting the values of Cosecant θ (Cosec θ) and Cotangent θ (Cot θ) in equation (iv)

Cosec2 θ = Cot2 θ + 1
Cot θ and Cosec θ are not defined for θ = 0°

So the above equation is true for all θ such that 0° < θ ≤ 90°

Using these identities, we can convert each trigonometric ratio in terms of other trigonometric ratios, that is, if any one of the ratios is known, we can also find the values of other trigonometric ratios.

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