# Examples of trigonometric identities with solutions

## What are the examples of trigonometric identities?

**Summarizing Trigonometric Identities**

- cos 2 θ + sin 2 θ = 1 cos 2 θ + sin 2 θ = 1.
- 1 + cot 2 θ = csc 2 θ 1 + cot 2 θ = csc 2 θ
- 1 + tan 2 θ = sec 2 θ 1 + tan 2 θ = sec 2 θ

## What are the 12 trigonometric identities?

**Sum and Difference of Angles Trigonometric Identities**

- sin(α+β)=sin(α). cos(β)+cos(α). sin(β)
- sin(α–β)=sinα. cosβ–cosα. sinβ
- cos(α+β)=cosα. cosβ–sinα. sinβ
- cos(α–β)=cosα. cosβ+sinα. sinβ
- tan. ( α + β ) = tan β 1 – tan α . tan. β
- tan. ( α – β ) = tan β 1 + tan α . tan.

## How do you solve trigonometric identities?

**5 strategies you can use to solve TRIG IDENTITIES**

- See what you can FACTOR. Sometimes, factoring with a common term will make everything into a trig identity. …
- Multiply the denominator by a CONJUGATE. …
- Get a COMMON DENOMINATOR. …
- SPLIT UP A FRACTION into two separate fractions. …
- Rewrite everything in terms of SINE AND COSINE.

## What are the 10 trigonometric identities?

**Practice Questions From Class 10 Trigonometry Identities**

- Prove √(sec θ – 1)/(sec θ + 1) = cosec θ – cot θ
- Prove (tan θ + sec θ – 1)/(tan θ – sec θ + 1) = (1 + sin θ)/cos θ
- Prove sec θ√(1 – sin
^{2}θ) = 1. - Given, √3 tan θ = 3 sin θ. Prove sin
^{2}θ – cos^{2}θ = 1/3. - Evaluate cos
^{2}θ tan^{2}θ + tan^{2}θ sin^{2}θ in terms of tan θ.

## What is the easiest way to learn trigonometric identities?

## What are the 6 trigonometric identities?

The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant and Cotangent.

## What is the easiest way to solve trigonometric identities Class 10?

**Make a point of memorizing them.**

- Quotient Identities: tan(x) = sin(x)/cos(x) cot(x) = cos(x)/sin(x)
- Reciprocal Identities: csc(x) = 1/sin(x) sec(x) = 1/cos(x) cot(x) = 1/tan(x) sin(x) = 1/csc(x) …
- Pythagorean Identities: sin
^{2}(x) + cos^{2}(x) = 1. cot^{2}A +1 = csc^{2}A. 1+tan^{2}A = sec^{2}A.

## How many identities are there in trigonometry class 11?

Basically, Trigonometry is defined with

**six**main ratios, namely Sine(sin), Cosine(cos), Tangent(tan), Cosecant(cosec), Secant(sec) and Cotangent(cot).## What are the 6 reciprocal identities?

**The formulas of the six main reciprocal identities are:**

- sin x = 1/cosec x.
- cos x = 1/sec x.
- tan x = 1/cot x.
- cot x = 1/tan x.
- sec x = 1/cos x.
- cosec x = 1/sin x.

## What are the 3 identities of trigonometry?

The main trigonometric identities are Pythagorean identities, reciprocal identities, sum and difference identities, double angle and half-angle identities. For the non-right-angled triangles, we will have to use the sine rule and the cosine rule.

## What are all the formulas of trigonometry?

**Basic Trigonometric Function Formulas**

- sin θ = Opposite Side/Hypotenuse.
- cos θ = Adjacent Side/Hypotenuse.
- tan θ = Opposite Side/Adjacent Side.
- sec θ = Hypotenuse/Adjacent Side.
- cosec θ = Hypotenuse/Opposite Side.
- cot θ = Adjacent Side/Opposite Side.

## What is cot θ is equal to?

The reciprocal tangent function is cotangent, expressed two ways: cot(theta)=

**1/tan(theta)**or cot(theta)=cos(theta)/sin(theta).## Who is the father of trigonometry?

mathematician Hipparchus

The first known table of chords was produced by the Greek mathematician

**Hipparchus**in about 140 BC. Although these tables have not survived, it is claimed that twelve books of tables of chords were written by Hipparchus. This makes Hipparchus the founder of trigonometry.## Is csc sin or cos?

The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x:

**csc x = 1 sin x**.## What is equal to Tanθ?

tan θ =

**sin θ / cos θ**## What is cosec (- theta?

Cosec theta of a right-angled triangle is equal to

**the ratio of the length of the hypotenuse to the length of the opposite side**.