If `cos alpha+cos beta=1/3`and `sin alpha+sin beta=1/4`,show that
`tan((alpha+beta)/2)=3/4`

If cosalpha+cosbeta=0=sinalpha+sinbeta,cos2alpha+cos2beta is equal to a) -2sin(alpha+beta) b) 2cos(alpha+beta) c) 2sin(alpha-beta) d) -2cos(alpha+beta)

If cos alpha + 2cos beta+ 3 cos gamma = 0, sin alpha + 2sin beta +3 sin gamma= 0 and alpha + beta + gamma= pi , then sin 3alpha + 8 sin 3 beta + 27 sin 3 gamma =

If (cos^4 alpha)/(cos^2beta)+(sin^4alpha)/(sin^2beta)=1 ,then prove that sin^4alpha+sin^4beta=2sin^2alphasin^2beta .

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]|

If (cos^4 alpha)/(cos^2beta)+(sin^4alpha)/(sin^2beta)=1 ,then prove that (cos^4beta)/(cos^2alpha)+(sin^4beta)/(sin^2alpha)=1

The distance between the points (a cos alpha, a sin alpha) and (a cos beta, a sin beta) is a) 2|sin((alpha-beta)/(2))| b) 2|a sin((alpha-beta)/(2))| c) 2|a cos((alpha-beta)/(2))| d) |a cos((alpha-beta)/(2))|

If cot alpha cot beta=2 , show that (cos (alpha+beta))/(cos (alpha-beta))=(1)/(3)