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

Prove that cos(alpha+beta )=cosalphacosbeta-sinalphasinbeta

By vector method, prove that cos (alpha+Beta) = cosalphacosBeta-sinalphasinBeta .

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

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

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

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 tan(alpha-beta)=(tanalpha-tanbeta)/(1+tanalphatanbeta)

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

Prove that tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)