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

Prove: sin^4 theta - cos^4theta = 1 - 2cos^2 theta

The value of 3(cos theta-sin theta)^(4)+6(sin theta+cos theta)^(2)+4 sin^(6) theta is where theta in ((pi)/(4),(pi)/(2)) (a) 13-4cos^(4) theta (b) 13-4cos^(6) theta (c) 13-4cos^(6) theta+ 2 sin^(4) theta cos^(2) theta (d) 13-4cos^(4) theta+ 2 sin^(4) theta cos^(2) theta

Prove that sin (30^(@) + theta) + cos (60^(@) + theta) = cos theta

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

Prove: (cos^2theta)/(1-tan theta) + (sin^3 theta)/(sin theta - cos theta ) = 1 + sin theta cos theta

Prove : (cos^2theta)/(1-tan theta) + (sin^3theta)/(sintheta - cos theta) = 1 + sin theta cos theta

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

Prove that cos 8 theta cos 2 theta = cos^(2) 5theta- sin^(2) 3 theta

Prove that (sin theta -cos theta+1 )/( sin theta + cos theta -1) =(1)/( sec theta -tan theta ) [use the identity sec ^(2) theta =1 +tan ^(2) theta ]

Prove the following: (sin theta - cos theta + 1 )/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)