" if "sin a=(1)/(2)" prove that "(3cos alpha-4cos^(2)alpha)=0

If sin alpha =(1)/(2) , prove that (3 cos alpha - 4 cos ^(3) alpha )=0.

If cos alpha+cos beta=(1)/(3) and sin alpha+sin beta=(1)/(4) prove that cos[(alpha-beta)/(2)]=+-((5)/(24))

If alpha= (2pi)/(7) , then prove that cos alpha+ cos 2 alpha+ cos 4alpha=-(1)/(2) . Hence, deduce that sin alpha+ sin 2alpha+ sin 4alpha=(sqrt(7))/(2)

For alpha , beta in R , prove that (cos alpha + cos beta )^(2)+ (sin alpha + sin beta )^(2)=4cos^(2). ((alpha-beta))/(2)

If y = (2 sin alpha )/(1 + cos alpha + sin alpha) then, prove that (1 - cos alpha + sin alpha)/(1 + sin alpha) = y .

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

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

If cos alpha+cos beta=0=sin alpha+sin beta. Prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

If cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

If cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)