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