`cos(n+1) alpha * cos(n-1)alpha + sin (n+1)alpha * sin (n-1) alpha = `

( sin(n+1) alpha - sin (n-1)alpha )/( cos (n+1) alpha + 2 cos n alpha + cos (n-1) alpha )=

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 ]

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

If A_(alpha)=[[cos alpha, sin alpha],[ -sin alpha , cos alpha]] , then prove that i) A_(alpha ). A_(beta)=A_(alpha + beta) ii) (A_alpha)^n=[[cos n alpha, sin n alpha],[ -sin n alpha, cos n alpha]] for every positive integer n .

If alpha-beta=(2n+1)(pi)/2, n epsilon Z then [(cos^(2) alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)][(cos^(2) beta, cos beta sin beta),(cos beta sin beta, sin^(2) beta)]=

If a cos^(3)alpha+3a cos alpha sin^(2)alpha=m and a sin^(2)alpha+3a cos^(2)alpha sin alpha=n then (m+n)^((2)/(3))+(m-n)^((2)/(3))=

If (2sin alpha) / ({1 + cos alpha + sin alpha}) = y, then ({1-cos alpha + sin alpha}) / (1 + sin alpha) =

If A=[cos alpha+sin alpha sqrt(2)sin alpha-sqrt(2)sin alpha cos alpha-sin alpha], prove that =[cos n alpha+sin n alpha sqrt(2)sin n alpha-sqrt(2)sin n alpha cos n alpha-sin n alpha] for all n in N.

If a cos^(3)alpha+3a cos alpha sin^(2)alpha=ma sin^(3)alpha+3a cos^(2)alpha sin alpha=n, then (m+n)^((2)/(3))+(m-n)^((2)/(3))=