By vector method, Prove that sin(alpha-beta)=sinalphacosbeta-cosalphasinbeta

Using vector method, prove cos(alpha-beta)=cosalphacosbeta+sinalphasinbeta.

By geometrical interpretation, prove that (i) sin(alpha+beta)=sin alpha cos beta+sinbeta cosalpha (ii) cos(alpha+beta)=cosalpha cosbeta -sin alpha sinbeta

Prove by vector method that sin(alpha+beta)=sinalphacosbeta+cosalphasinbeta.

Prove that |cosalpha-cosbeta|lt=|alpha-beta|

Prove that (cos alpha+cos beta)^(2)+(sin alpha -sin beta)^(2)=4 cos^(2) ((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 cosalpha+cosbeta+cosgamma=0a n da l sosinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0 sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

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

If (cos alpha)/(cos A)+(sin alpha)/(sin A)+(sin beta)/(sin A)=1 , where alpha and beta do not differ by an even multiple of pi , prove that (cos alpha cos beta)/(cos^(2)A)+(sin alpha sin beta)/(sin^(2)A)=