Prove that `sin^(4) alpha + cos^(4) alpha + 2 sin^(2) alpha cos^(2) alpha = 1`.

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 :

The angle between the lines sin^(2) alpha.y^(2) -2xy.cos^(2) alpha + (cos^(2) alpha -1)x^(2) =0 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 alpha lt 2 sin^(-1) x +cos^(-1)x le beta , then

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

If alpha le 2 sin^(-1) x + cos^(-1) x le beta , then

The angle between the lines x cos alpha + y sin alpha = a and x sin beta - y cos alpha = a is

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

The expression nsin^(2) theta + 2 n cos( theta + alpha ) sin alpha sin theta + cos2(alpha + theta ) is independent of theta , the value of n is