Consider three points `P = (-sin (beta-alpha), -cos beta)`, `Q = (cos(beta-alpha), sin beta)`, and `R = ((cos (beta - alpha + theta), sin (beta - theta))`, where `0< alpha, beta, theta < pi/4` Then

If cos alpha + cos beta =0 = sin alpha + sin beta , then cos 2 alpha + cos 2 beta is equal to

Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) ]:} =0

Under rotation of axes through theta , x cosalpha + ysinalpha=P changes to Xcos beta + Y sin beta=P then . (a) cos beta = cos (alpha - theta) (b) cos alpha= cos( beta - theta) (c) sin beta = sin (alpha - theta) (d) sin alpha = sin ( beta - theta)

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

If f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|, then

If ( cos x - cos alpha)/(cos x - cos beta) = ( sin^2 alpha cos beta)/(sin^2 beta cos alpha) then cos x =

The distance between the points ( a cos alpha, a sin alpha ) and ( a cos beta, a sin beta ) is

If cos theta=(cos alpha-cos beta)/(1-cos alpha cos beta), prove that tan theta/2=+-tan alpha/2 cot beta/2.

sin alpha+sinbeta=(1)/(4) and cos alpha+cos beta=(1)/(3) the value of sin(alpha+beta)

If cos alpha + cos beta = 1//2 and sin alpha+ sin beta = 1//3 , then