Question

$(1+sin^{2} )cosx+(1+cos^{2} x)sinx=1=sin2x$

Answer 1

The answer is = 1 + sin x

Explanation

we need

a^2 - b^2 = (a+b) (a-b)

we use

cos^2 x + sin^2 x = 1

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

therefore

cos ^2 x over 1 - sin x = 1+ sin x