If `A_alpha=[cosalphasinalpha-sinalphacosalpha]` , then prove that `A_alphaA_beta=A_(alpha+beta)` for every positive integer `n` .

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_(alpha)=[cos alpha sin alpha-sin alpha cos alpha], then prove that (A_(alpha))^(n)=[cositive in n alpha-s in n alpha cos n alpha] for every positive integer n.

If cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

If cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

Prove that |cos alpha-cos beta|<=| alpha-beta|

if 2tan beta+cot beta=tan alpha then prove that cot beta=2tan(alpha-beta)

If cos alpha+cos beta=0=sin alpha+sin beta. Prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

Prove that alpha^(2)+beta^(2)=(alpha+beta)^(2)-2 alpha beta

If 2tan beta+cot beta=tan alpha, prove that cot beta=2tan(alpha-beta)