`(cos ^(3) alpha - cos 3 alpha )/( cos alpha ) + (sin ^(3)alpha + sin 3 alpha )/( sin alpha ) = 3.`

(cos alpha + 2 cos 3 alpha + cos 5 alpha )/(cos 3 alpha + 2 cos 5 alpha + cos 7 alpha ) = cos 3 alpha sec 5 alpha .

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

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.

Show that 4 sin alpha.sin (alpha + pi/3) sin (alpha + 2pi/3) = sin 3alpha

If a cos^3 alpha +3acosalpha*sin alpha = m and a sin^3alpha +3a cos^3alpha sin^3alpha = n then (m + n)^(2/3) + (m-n)^(2/3)

If (2sinalpha)/({1+cos alpha+sin alpha})=y, then ({1-cos alpha+sin alpha})/(1+sin alpha)=

cos alpha cos(60^(@) - alpha ) cos (60^(@) + alpha ) = 1/4 cos 3 alpha.

If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)] and B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is null matrix, then alpha-beta is

Which is equivalent to (sin^2 alpha + cos^2 alpha )/(cos alpha ) ?