If `A = [[cos alpha,sin alpha],[-sin alpha,cos alpha]]` then prove that, AA'=I. Hence find `A^(-1)`.

If A=[(cos alpha, sin alpha),(-sin alpha, cos alpha)] , then verify that A'A=I

If A=[(sin alpha, cos alpha),(-cos alpha, sin alpha)] , then verify that A'A=I

If A=[(cos alpha, -sin alpha),(sin alpha, cos alpha)], and A+A'=I , then the value of alpha is

If A =[[cos alpha,-sin alpha],[sinalpha, cos alpha]] , B= [[cos 2 beta, sin 2 beta],[sin beta ,-cos beta]] where 0 lt beta lt pi/2 , then prove that BAB=A^(-1) . Also, find the least value of alpha of which BA^(4) B= A^(-1)

If tantheta=(sin alpha-cos alpha)/(sinalpha+cosalpha)1 then

A=[(cos alpha,-sin alpha),(sin alpha,cos alpha)] and A+A^(T)=I , find the value of alpha .

If sin alpha = sin beta and cos alpha = cos beta then-

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 .

If (sin alpha-cosalpha)/(sin alpha+cosalpha)=tan theta , then prove that sin prop + cos prop = pm sqrt(2)cos theta.