If `A_alpha=[cosalphasinalpha-sinalphacosalpha]` , then prove that `(A_alpha)^n=[cos n alpha sinn alpha-sinn alphacos n alpha]` for every positive integer `n` .

if A,=[[cos alpha,sin alpha-sin alpha,cos alphasin alpha,cos alphacos2 alpha,sin2 alpha-sin2 alpha,cos2 alpha]]

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

|[ Prove that 0,cos alpha,-sin alphasin alpha,0,cos alphacos alpha,sin alpha,0cos alpha,sin alpha,0 where x=sin alpha cos alpha

If A_alpha=[cosalphasinalpha-sinalphacosalpha],t h e nA_alphaA_beta= (a)A_(alpha+beta) (b) A_(alphabeta) (c) A_(alpha-beta) (D) None of these

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.

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

If cot alpha+tan alpha=m and (1)/(cos alpha)-cos alpha=n, then

If m cos alpha-n sin alpha=p then prove that m sin alpha+n cos alpha=+-sqrt(m^(2)+n^(2)-p^(2))

If sin alpha+cosec alpha=2 ,find the value of sin^(n)alpha+cosec^(n)alpha , n in Z

if cos^(2)alpha-sin alpha=(1)/(n) then alpha