If `sin alpha-sin beta=1//3` and `cos beta-cos alpha=1//2`, show that `cot(alpha+beta)=(2)/(3)`.

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

Let alpha, beta" such that "pi lt alpha-beta lt 3pi." If sin "alpha+sin beta=-21//65 cos alpha+cos beta=-27//65 , then find the value of cos ""(alpha-beta)/(2) .

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

If (sin alpha)/(sin beta)=(cos gamma)/(cos delta), then (sin ((alpha-beta)/2) . cos ((alpha+beta)/2) . cos delta)/(sin ((delta-gamma)/2) . sin ((delta+gamma)/2) . sin beta)

If cos alpha + cos beta + cos gamma = sin alpha + sin beta + sin gamma = 0 , show that cos 3alpha + cos 3 beta + cos gamma = 3 cos (alpha + beta + gamma) and

If cos (alpha - beta) + cos (beta - gamma) + cos (gamma - alpha) = (-3)/(2) then prove that cos alpha + cos beta+ cos gamma = sin alpha + sin beta + sin gamma = 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)

If alpha , beta in (0,pi/2), sin alpha =4/5 and cos ( alpha + beta) = ( -12)/(13) then sin beta is equal to