`|(sin^2theta,cos^2theta),(-cos^2theta,sin^2theta)|=`

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

If |(1+sin^2 theta,sin^2 theta,sin^2 theta),(cos^2 theta,1+cos^2 theta,cos^2 theta),(4sin 4 theta,4sin4theta,1+4sin4theta)|=0, then ... sin 4theta equal to ....

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

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

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

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

(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?

Prove that : cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)

Prove that : sin^(2)theta+cos^(4)theta=cos^(2)theta+sin^(4)theta

The value of cos^4theta+sin^4theta-6cos^2theta is (a) cos2theta (b) sin2theta (c) cos4theta (d) none of these