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

Prove , using mean value theorem, that |sin alpha -sin beta | le| alpha-beta|, alpha, beta in RR .

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

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

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

Prove that |2alpha+beta+gamma+deltaalphabeta+gammadeltaalpha+beta+gamma+delta2(alpha+beta)(gamma+delta)alphabeta(gamma+delta)+gammadelta(alpha+beta)alphabeta+gammadeltaalphabeta(gamma+delta)+gammadelta(alpha+beta)2alphabetagammadelta|=0

Prove that cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos((alpha+beta)/2)cos((beta+gamma)/2)cos((gamma+alpha)/2)

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

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

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

If sin^4alpha+cos^4beta+2=4sinalphacosbeta,0lt=alpha,betalt=pi/2 then find the value of (sinalpha+cosbeta)dot