Q13/072) find the period of (sinx)^4+(cosx)^4

(sinx)^4+(cosx)^4 = ( sin ^2 x + cos^2 x) - 2 sin ^2 x cos ^2 x
= 1 - 2 sin ^2 x cos ^2 x
= 1- 1/2( 4 sin ^2 x cos ^2 x)
= 1 - 1/2( sin 2x)^2 
= 1/2( 2 - sin ^2 2x)
= 1/4( 4 - 2 sin ^2 2 x)
= 1/4( 3 + cos 4x)

now cos x has period 2pi so cos 4x has period pi/2 hence (sinx)^4+(cosx)^4 has period pi/2