Solve sin2xcos2x12 Find the exact solutions for 0

Solve sin²x+cos2x=1/2

Find the exact solutions for 0</=x</=2pi

Solution

Sin ²x +cos 2x=1/2

sin^2x+1-2sin^2x=1/2

1-sin^2x=1/2

2-2sin^2x=1

1-2sin^2x=0

sin^2x=1/2

sin x=+-1/sqrt2

x=pi/4,3pi/4,5pi/4,7pi/4