sec^(2)theta-(sin^(2)theta-2sin^(4)theta)/(2cos^(4)theta-cos^(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)

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 :

"(i) "sin^(4)theta-cos^(4)theta=sin^(2)theta-cos^(2)theta

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

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

If tan theta=(3)/(4), then (4sin^(2)theta-2cos^(2)theta)/(4sin^(2)theta+3cos^(2)theta)

If tan theta=(3)/(4), then (4sin^(2)theta-2cos^(2)theta)/(4sin^(2)theta+3cos^(2)theta)

Prove that sin^(4)theta-cos^(4)theta=sin^(2)theta-cos^(2)theta