P=(1)/(2)sin^(2)theta+(1)/(3)cos^(2)theta," then "

sin ^ (4) theta + 2sin ^ (2) theta (1- (1) / (cos ec ^ (2) theta)) + cos ^ (4) 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)

Prove the following 1.((1-cos^(2)theta)/(sin^(2)theta))=12.1-((cos^(2)theta)/(1+sin theta))=sin theta

If sin theta + cos theta = and sin^(3) theta + cos^(3)theta = q, then p(p^(2) - 3) =

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

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)/(3)) , then value of theta is