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

Prove that (3 + cos 4theta) cos 2theta = 4(cos^(8)theta - sin^(8)theta) .

2 cos theta - cos 3 theta - cos 5 theta - 16 cos^(3) theta sin^(2) theta =

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

Prove that : cos2 theta= cos^2 theta-sin^2 theta=1-2 sin^2 theta= 2 cos^2 theta-1 .

Prove that ( cos theta + cos 2 theta + cos 3 theta + cos 4 theta)/(sin theta + sin 2 theta + sin 3 theta + sin 4 theta)= cot ""(5theta)/(2).

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

2cos theta-cos3 theta-cos5 theta-16cos^(3)theta sin^(2)theta=

2cos theta-cos3 theta-cos5 theta-16cos^(3)theta sin^(2)theta=

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

If theta be any real, prove that : cos4 theta=1-8 sin^2 theta cos^2 theta =1-8 cos^2 theta +8 cos^4 theta .