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] , [sin alpha, cos alpha]], B=[[cos2beta, sin 2beta] , [sin 2 beta, -cos2beta]] where 0 lt beta lt pi/2 then prove that BAB=A^(-1) Also find the least positive value of alpha for which BA^4B= A^(-1)

If sin 3 alpha =4 sin alpha sin (x+alpha ) sin(x-alpha ) , then

If sin theta= sin alpha , then

If A=[(0,-tan (alpha/2)),(tan (alpha/2),0)] and I is 2 xx 2 unit matrix, then (I-A)[(cos alpha,-sin alpha),(sin alpha, cos alpha)] is

If sin alpha, sin^(2) alpha, 1,sin^(4) alpha, sin^(5) alpha, ( - pi lt alpha lt pi ) are in A.P. , then alpha lies in the interval :

"Evaluate "Delta ={:|( 0 , sin alpha ,-cos alpha ) ,( -sin alpha , 0 , sin beta ),( cos alpha , -sin beta , 0)|:}

Find the inverse of each of the matrices (if it exists ) {:[( 1,0,0),( 0 ,cos alpha , sin alpha ),( 0, sin alpha , -cos alpha ) ]:}

If A_(theta) = [(cos theta ,sin theta ),(-sin theta ,cos theta )] then A_(alpha)A_(beta) equals :