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

if [ ( cos alpha, - sin alpha),(sin alpha, cos alpha)] and A +A^1 =I then alpha =……

If cot (alpha + beta )=0 , then sin(alpha+2beta ) =

If cosalpha+cosbeta=0=sinalpha+sinbeta, then prove that cos2alpha+cos2beta=-2cos(alpha+beta) .

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

alpha is a root of equation ( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta is a root of the equation 3 cos 2x - 10 cos x +3 =0 and gamma is a root of the equation 1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 cos alpha + cos beta + cos gamma can be equal to

Prove that 2tanbeta+cotbeta=tanalphaimplies2tan(alpha-beta)=cotbeta .

if tanbeta=(nsinalphacosbeta)/(1-nsin^2alpha) then prove that tan(alpha-beta)=(1-n)tanalpha.

The value of the determinant |{:(1,sin(alpha-beta)theta,cos (alpha-beta)theta),(a, sinalphatheta,cos alphatheta),(a^(2),sin(alpha-beta)theta,cos(alpha-beta)theta):}| is independent of

Find distance PQ between the points P ( a cos alpha, a sin alpha) and Q ( a cos beta, a sin beta) .