How do I prove that sin^2x + tan^2xsin^2x = tan^2x ?

2 Answers
Sep 20, 2015

Use tan x = sin x / cos x and sin^2 x + cos^2 x = 1 and rearrange.

Explanation:

By definition:

tan x = sin x / cos x

and by Pythagoras:

sin^2 x + cos^2 x = 1

So:

tan^2 x = sin^2 x / cos^2 x = sin^2 x / cos^2 x(cos^2 x + sin^2 x)

= (sin^2x cos^2x)/cos^2 x + (sin^2 x sin^2 x) / cos^2 x

= sin^2 x + sin^2 x tan^2 x

Sep 20, 2015

Using the rules: tanx = sinx/cosx

sin^2x + cos^2x = 1

Explanation:

sin^2x + tan^2x.sin^2x = tan^2x

sin^2x + sin^4x/(cos^2x) = tan^2x

sin^2x + sin^4x/(cos^2x) = sin^2x/(cos^2x)

sin^2x = (sin^2x - sin^4x)/(cos^2x)

sin^2x = sin^2x (( 1 - sin^2x))/(cos^2x)

sin^2x = sin^2x (cos^2x) / (cos^2x)

sin^2x = sin^2x