verify the identity:

Question

(1+sec^2x)/(1+tan^2x)=1+cos^2x

Answer 1

The trignometric identity is ( 1+sec^2x)/(1+tan^2x) = 1+cos^2x

Pythagorean identity is 1+tan^2x = sec^2x

( 1+sec^2x)/(1+tan^2x) = ( 1+sec^2x)/sec^2x

= (1/sec^2x)+(sec^2x/sec^2x)

= cos^2x+1

( 1+sec^2x)/(1+tan^2x) = 1+cos^2x.