Prove that `cos(alpha-beta)/(cos alpha sin beta)=tan alpha+cot beta`

Prove that (tan alpha+tan beta)/(cot alpha+cot beta)=tan alpha tan beta

Prove that (cos2 alpha-cos 2 beta)/(sin2 alpha+sin2 beta)=tan(beta-alpha)

Prove by vectors that : cos (alpha - beta) = cos alpha cos beta+ sin alpha sin beta .

Prove by vectors that : cos (alpha + beta) = cos alpha cos beta- sin alpha sin beta .

Using vectors prove that sin(alpha - beta) = sin alpha cos beta- cos alpha sin beta .

Using vectors, prove that sin (alpha+beta)=sin alpha cos beta+ cos alpha sin beta .

Find the value of sin (alpha - beta), cos (alpha -beta) and tan (alpha - beta), given cos alpha = (-12)/(13) , cot beta = (24)/(7), alpha in Quadrant II, beta in Quadrant I.

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

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

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