Eliminate `alpha` between the equations:
`(sin^2 alpha)/(cos alpha)=a^3` and `(cos^2 alpha)/(sin alpha)= b^3`.

Statement I The system of linear equations x+(sin alpha )y+(cos alpha )z=0 x+(cos alpha ) y+(sin alpha )z=0 -x+(sin alpha )y-(cos alpha )z=0 has a not trivial solution for only one value of alpha lying between 0 and pi . Statement II |{:(sin x, cos x , cos x),( cos x , sin x , cos x) , (cos x , cos x , sin x ):}|=0 has no solution in the interval -pi//4 lt x lt pi//4 .

Let lambda and alpha be real. Then the numbers of intergral values lambda for which the system of linear equations lambdax +(sin alpha) y+ (cos alpha) z=0 x + (cos alpha) y+ (sin alpha) z=0 -x+(sin alpha) y -(cos alpha) z=0 has non-trivial solutions is

One side of a square makes an angle alpha with x axis and one vertex of the square is at origin. Prove that the equations of its diagonals are x(sin alpha+ cos alpha) =y (cosalpha-sinalpha) or x(cos alpha-sin alpha) + y (sin alpha + cos alpha) = a , where a is the length of the side of the square.

If tan theta=(sin alpha- cos alpha)/(sin alpha+cos alpha) , then:

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

Find the value of f(alpha, beta) =|(cos (alpha + beta), -sin (alpha + beta), cos 2beta),(sin alpha, cos alpha, sin beta),(-cos alpha, sin alpha, cos beta)|

If sin (3alpha) /cos(2alpha) < 0 If alpha lies in

If (cos^4 alpha)/(cos^2 beta)+ (sin^4 alpha)/(sin^2 beta) =1 , prove that : (cos^4 beta)/(cos^2 alpha)+ (sin^4 beta)/ (sin^2 alpha) =1 .

Let f(alpha, beta) = =|(cos (alpha + beta), -sin (alpha + beta), cos 2beta),(sin alpha, cos alpha, sin beta),(-cos alpha, sin alpha, cos beta)| if i =int_(-pi//2)^(pi//2) cos ^(2)beta(f(0,beta)+f(0,(pi)/(2)-beta))dbeta then i is

Find A^2 if A = [(cos alpha, sinalpha),(-sin alpha, cos alpha)]