How to prove this identity? sin^2x+tan^2x * sin^2x= tan^2x

2 Answers
Mar 18, 2018

Shown below...

Explanation:

Use our trig identities...

sin^2 x + cos^2 x =1

=> sin^2 x / cos^2 x + cos^2 x / cos^2 x = 1 / cos^2 x

=> tan^2 x + 1 = 1/cos^2 x

Factor the left side of your problem...

=> sin^2 x ( 1 + tan^2 x )

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

=> (sinx/cosx)^2 = tan^2 x

Mar 18, 2018

Given,

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

=sin^2 x(1+tan^2 x)

=sin ^2 x sec ^2x (as, sec^2x - tan^2 x=1)

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

=tan^2 x

              Proved