Question

(1-sin(x))(1+sin(x))=1/1+tan(x^2) Prove that the statement is an identity

Answer 1

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

I think  the right side is  tan^2 x    ( the square of tan x)

Left side =  1 - sin^2 x

Right side = 1  / ( 1 + (sin^2 x / cos^2x))

= 1  /    (cos^2x + sin^2x) / cos^2 x

Now sin^2 x + cos^2 x = 1  so

this =  1  /   1 / cos^2x

= cos^2x  = 1 - sin^2 x  = Left side    - Proved