If `cos theta+cos^(2)theta=1` then `sin^(2)theta+2sin^(2)theta+sin^(2)theta=`

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

sin^(4)theta+cos^(4)theta=1-2sin^(2)theta cos^(2)theta

2(cos theta+cos2 theta)+(1+2cos theta)sin2 theta=2sin theta

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)

If |{:(1+cos^(2)theta,sin^(2)theta,4cos6theta),(cos^(2)theta,1+sin^(2)theta,4cos6theta),(cos^(2)theta,sin^(2)theta,1+4cos6theta):}|=0 , and theta in (0,(pi)/(2)) , then value of theta is

Prove that sin^(2)theta+sin^(2)2 theta+sin^(2)3 theta+....+sin^(2)n theta=(n)/(2)-(sin n theta cos(n+1)theta)/(2sin theta)

A value of theta satisfying 4cos^(2)theta sin theta-2sin^(2)theta=3sin theta is