` cos 4 alpha = 1- 8 cos^2 alpha +8 cos^4 alpha `

Prove that sin^(4) alpha + cos^(4) alpha + 2 sin^(2) alpha cos^(2) alpha = 1 .

( cos 2 alpha)/( cos^(4) alpha - sin^(4) alpha ) -(cos^(4) alpha + sin^(4) alpha )/(2-sin^(2) 2alpha ) =

1/(cos alpha + cos 3 alpha)+ 1/(cos alpha + cos 5 alpha)+ 1/(cos alpha + cos 7 alpha) +....+ 1/(cos alpha +cos(2n+1) alpha) = 1/2 "cosec" alpha[tan (n+1) alpha - tan alpha ]

cos4x-cos4 alpha = 8 (cos x-cos alpha) (cos x + cos alpha) (cos x-sin alpha) (cos x + sin alpha

(( cos alpha - cos 3 alpha ) ( sin 8 alpha + sin 2 alpha ))/( ( sin 5 alpha - sin alpha ) ( cos 4 alpha - cos 6 alpha ))=

( sin 8 alpha * cos alpha - sin 6 alpha * cos 3 alpha )/(cos 2 alpha cos alpha - sin 3 alpha * sin 4alpha ) =

If n=1,2,3,……. then cos alpha cos 2 alpha cos 4 alpha ……. Cos 2^(n-1) alpha is equal to

If alpha = (pi)/(13), Prove that cos alpha cos 2alpha cos 3alpha cos 4alpha cos 5alpha cos 6alpha = (1)/(64) .

If sin alpha/2 + cos alpha/2=1.4 , then: sin alpha cos alpha =