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)] , then verify that A'A=I

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

If sin theta= sin alpha , then

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

Find distance between the pair of points given. (i) (a sin alpha, - b cos alpha) , ( - a cos alpha , b sin alpha ) (ii) ( a + b, b + c) , (a - b , c - b) (iii) ( 4, 10) , (7 - 6 )

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)|:}

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 alpha)^(x)+(cos alpha)^(x) ge 1,0 lt a lt (pi)/(2) then