`(sin(theta/2)-cos(theta/2))^(2)=1-sin theta`

Prove the following identities: sin^(8)theta+cos^(8)theta=(sin^(2)theta-cos^(2)theta)(1-2sin^(2)theta cos^(2)theta)

Prove related problems - Type 1 -prove the following identities (1)sin^(8)theta-cos^(8)theta=(sin^(2)theta-cos^(2)theta)(1-2sin^(2)theta cos^(2)theta(2)cot^(2)theta+cot^(4)theta=cos ec^(4)theta-cos ec^(2)theta

((sin theta+cos theta)^(2)-1)/(sin theta*cos theta)

(sin theta-cos theta)^(2)*(sin theta+cos theta)^(2)=

(2sin theta*cos theta-cos theta)/(1-sin theta+sin^(2)theta-cos^(2)theta)=cot theta

Prove that (1-sin theta+cos theta)^(2)=2(1+cos theta)(1-sin theta)

(1+sin2 theta-cos2 theta)/(1+sin2 theta+cos2 theta)=tan theta

(sin theta-cos theta)/(sin theta+cos theta)+(sin theta+cos theta)/(sin theta-cos theta)=(2)/((2sin^(2)theta-1))

(cos^(2)theta(1-cos theta))/(sin^(2)theta(1-sin theta))=(1+sin theta)/(1+cos theta)