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### Course: Class 10 (Old) > Unit 8

Lesson 5: Trigonometric identities- Intro to Pythagorean trigonometric identities
- Converting between trigonometric ratios example: write all ratios in terms of sine
- Evaluating expressions using basic trigonometric identities
- Trigonometric identity example proof involving sec, sin, and cos
- Trigonometric identity example proof involving sin, cos, and tan
- Trigonometric identity example proof involving all the six ratios
- Trigonometric identities challenge problems

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# Trigonometric identity example proof involving sin, cos, and tan

Let's try to prove a trigonometric identity involving sin, cos, and tan in real-time and learn how to think about proofs in trigonometry. Created by Aanand Srinivas.

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- you rewrite 1-tan^2 y as 1- (sin^2y/cos^2y) and do the same for the 1+tan^2y you will end up with (cos^2y-sin^2y)/(cos^2y + sin^2y) then using the trigonometric identities cos^2y-sin^2y = cos(2y) and cos^2y + sin^2y = 1 you will end up with cos(2y)/1 which is equal to cos2y(1 vote)
- cos 2y= 1-tan^2y/1+tan^2y(0 votes)
- you rewrite 1-tan^2 y as 1- (sin^2y/cos^2y) and do the same for the 1+tan^2y you will end up with (cos^2y-sin^2y)/(cos^2y + sin^2y) then using the trigonometric identities cos^2y-sin^2y = cos(2y) and cos^2y + sin^2y = 1 you will end up with cos(2y)/1 which is equal to cos2y(2 votes)

- sir how do those ideas strike u. they cant strike me...so do i have to practice(0 votes)