# Trigonometric Ratio and Identities

By Dhruv Kumar|Updated : July 29th, 2021

In Mathematics, trigonometry is one of the important chapters carrying second highest weightage after Algebra. The questions from trigonometry require rigorous practice and command on concepts to get high marks in this exam because these questions are not very general and straight-forward in nature.  To solve these questions, you must be aware of the basics of trigonometry ratio and identity so that maximum questions can be attempted in the given time frame.

In Mathematics, trigonometry is one of the important chapters carrying second highest weightage after Algebra. The questions from trigonometry require rigorous practice and command on concepts to get high marks in this exam because these questions are not very general and straight-forward in nature.  To solve these questions, you must be aware of the basics of trigonometry ratio and identity so that maximum questions can be attempted in the given time frame.

In this article, we will discuss some important formula and short notes and basics of trigonometry ratio and identity  to solve trigonometry questions of quickly during the NDA exam.

Trigonometry is very simple if you study it very well and in a systematic manner and clear of concept of trigonometry  it helps in during the NDA exam . Let us understand the basics of trigonometry one by one as described below-

I . Trigonometric Ratios –

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

The trigonometry ratios for a specific angle ‘’ is given below: Trigonometry ratio table:

The trigonometric ratios for some specific angles such as 0 °, 30 °, 45 °, 60 ° and 90° are given below, which are commonly used in mathematical calculations.

From this table, we can find the value for the trigonometric ratios for these angles

Trigonometric Ratios Identities:

There are many trigonometric ratios identities that we use to make our calculations easier and simpler. These include identities of complementary angles, supplementary angles, Pythagorean identities, and sum, difference, product identities.

Trigonometric Ratios of Complementary Angles

The complementary angles are a pair of two angles such that their sum is equal to 90°. The complement of an angle  is. The trigonometric ratios of complementary angles are:

Trigonometric Ratios of Supplementary Angles

The supplementary angles are a pair of two angles such that their sum is equal to 180°. The supplement of an angle is. The trigonometric ratios of supplementary angles are:

Pythagorean Trigonometric Ratios Identities

The Pythagorean trigonometric ratios identities in trigonometry are derived from the Pythagoras thermo Applying Pythagoras theorem to the right-angled triangle below, we get:

Dividing both sides by

we can derive two other Pythagorean trigonometric ratios identities:

Sum, Difference, Product Trigonometric Ratios Identities

The sum, difference, and product trigonometric ratios identities include the formulas of sin(A+B), sin(A-B), cos(A+B), cos(A-B), etc.

Half, Double, and Triple-Angles Trigonometric Ratios Identities

Double Angle Trigonometric Ratios Identities

The double angle trigonometric identities can be obtained by using the sum and difference formulas.

For example, from the above formula sin (A+B) = sin A cos B + cos A sin B

Substitute A = B =  on both sides here, we get:

In the same way, we can derive the other double angle identities.

Half Angle Trigonometric Ratios Identities:

Using one of the above double angle formulas,

Replacing  by on both sides,

This is the half-angle formula of sine

In the same way, we can derive the other half-angle formulas.

Triple Angle Trigonometric Ratios Identities

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