Prove the following identities: `sin^8theta-cos^8theta=(sin^2theta-cos^2theta)(1-2sin^2thetacos^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^(3)theta+cos^(3)theta)/(sin theta+cos theta)+sin theta cos theta=1

sin^4theta+2sin^2thetacos^2theta=1-cos^4 theta

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

Prove the following identities: 2(sin^(6)theta+cos^(6)theta)-3(sin^(4)theta+cos^(4)theta)+1=0sin^(6)theta+cos^(6)theta+3sin^(2)theta cos^(2)theta=1(sin^(8)theta-cos^(8)theta)=(sin^(2)theta-cos^(2)theta)(1-2sin^(2)theta cos^(2)theta)

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

Find the value of (sin^4theta+cos^4theta)/(1-2sin^2 thetacos ^2 theta)

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

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

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