[10sin^(4)theta+15cos^(4)theta=6],[27cos^(6)theta+8sin^(6)theta=?]

The value of sin^(8)theta+cos^(8)theta+sin^(6)theta cos^(2)theta+3sin^(4)theta cos^(2)theta+cos^(6)theta sin^(2)theta+3sin^(2)thetacos^(4)theta is equal to

The value of sin^(8)theta+cos^(8)theta+sin^(6)theta cos^(2)theta+3sin^(4)theta cos^(2)theta+cos^(6)theta sin^(2)theta+3sin^(2)thetacos^(4)theta is equal to

cos^(3)2 theta+3cos2 theta=4(cos^(6)theta-sin^(6)theta)

The value of (2(sin^(6)theta+cos^(6)theta)-3(sin^(4)theta+cos^(4)theta))/(cos^(4)theta-sin^(4)theta-2cos^(2)theta) is :

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)

A value of theta in (0, pi//3), for which |{:(1+"cos"^(2)theta, "sin"^(2)theta, 4"cos" 6 theta), ("cos"^(2)theta, 1+"sin"^(2)theta, 4"cos"6theta), ("cos"^(2)theta, "sin"^(2)theta, 1+4"cos"6theta):}| = 0, is

If sin theta + sin^(2) theta =1 then cos^(4) theta + cos^(8) theta + 2 cos^(6) theta =

sin^(6)theta+cos^(6)theta+3sin^(2)theta cos^(2)theta=1

If sin theta+sin ^(2) theta=1 then cos ^(12) theta+3 cos ^(10) theta+3 cos ^(8) theta+cos ^(6) theta=