Question

Question #b8301

Answer 1

`sin(pi/4-x)/sin(pi/4+x)`

Explanation:

For this expression, (cos x + sin x) is not zero. When# x = -pi/4 and x = 3pi/4, cos x + sin x = 0. .

`(cos 2x)/(1+sin 2x)=(cos^2x-sin^2x)/(cos^2x+sin^2x+2sin x cos x)=((cos x-sin x)(cos x+sin x))/(cos x+sin x)^2=(cos x-sin x)/(cos x+sin x)`
Divide numerator and denominator by`sqrt2` and use `sin(pi/4)=cos(pi/4)=1/sqrt2`
A simplified form is `sin(pi/4-x)/sin(pi/4+x)`.