Show by vector method that `sin(alpha-beta)=sinalphacosbeta-cosalpha sinbeta.`

Prove by vector methods that sin(alpha+beta)=sin alpha cos beta+cos alpha sin beta

Prove by vector metod the following formula of plane trigonometry cos(alpha-beta)=cosalpha cosbeta+sinalpha sinbeta

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

Show that 2"sin"^(2)beta+4 cos(alpha+beta)"sin" alpha sin beta+cos2(alpha+beta)=cos 2alpha .

Prove that |[cos alpha cos beta, cos alpha sin beta , sin alpha],[-sinbeta,cosbeta,0],[sinalpha cosbeta, sinalpha sinbeta, cos alpha]|=cos2alpha

Show without expanding at any stage that: [0,sinalpha-cosalpha],[-sinalpha,0,sinbeta],[cosalphas-sinbeta,0]|=0

If tan theta=(tan alpha+tan beta)/(1+tan alpha tan beta) then show that sin2 theta=(sin2 alpha+sin2 beta)/(1+sin2 alpha sin2 beta)

Evaluate: quad =|cos alpha cos beta cos alpha sin beta-sin alpha-sin beta cos beta0sin alpha cos beta sin alpha sin beta cos alpha|

If 0