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

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

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

Prove that cot^4 theta+ cot^2 theta= cosec^4 theta-cosec^2 theta

Prove the following identities: (tan theta-cot theta)/(sin theta cos theta)=sec^(2)theta-cos ec^(2)theta=tan^(2)theta-cot^(2)theta

(sin theta" cosec "theta tan theta cot theta)/(sin^(2)theta+cos^(2)theta)

Prove the following identities: (cos theta)/(1-sin theta)+(cos theta)/(1+sin theta)=2sec theta

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

Prove the following trigonometric identities: tan theta-cot theta=(2sin^(2)theta-1)/(sin theta cos theta)

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

Prove the following trigonometric identities: cot theta-tan theta=(2cos^(2)theta-1)/(sin theta cos theta)