Find the value of `sin^6 alpha+ cos^6 alpha+ 2sin^2 alpha cos^2 alpha`.

Calculate the value of (sin^(6)alpha +cos^(6) alpha + 3sin^(2) alpha cos^(2) alpha).

If alpha =(pi)/(18) radian then the value of (cos alpha + cos 2 alpha+ cos 3 alpha +…+ cos 18 alpha) is-

If n is a positive integer, then the value of (cos alpha cos 2 alpha cos 2 ^(2) alpha ….cos 2 ^(n-1)alpha) is-

Show that the image of the point (h,k) with respect to the striaight line x cos alpha+ y sin alpha=p is the point (2 p cos alpha- h cos2 alpha- k sin 2 alpha, 2p sin alpha- h sin 2 alpha- k cos 2 alpha) .

If alpha, beta , gamma are angles of a triangle then the value of (sin^(2) alpha + sin ^(2) beta+sin ^(2) gamma-2 cos alpha cos beta cos gamma) is-

If" " tan theta = (sin alpha - cos alpha)/(sin alpha + cos alpha),"prove that",2 cos^(2) theta = 1 + sin 2 alpha.

Provet that the producet of the matrics [[cos^2 alpha cos alpha sin alpha], [ cos alpha sin alpha sin^2 alpha]] and [[cos^2 beta cos beta sin beta], [ cos beta sin beta sin^2 beta]] is the null matrix when alpha and beta differ by an odd multiple of pi / 2 .

Prove that, (cos alpha + sin alpha)/(cos alpha -sin alpha)-(cos alpha - sin alpha)/(cos alpha + sin alpha) = 2 tan 2 alpha