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

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

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)

sin alpha-cos alpha=(1)/(3) then sin^(4)alpha-cos^(4)alpha=

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

If cos (alpha - beta) + cos (beta - gamma) + cos (gamma - alpha) = (-3)/(2) then prove that cos alpha + cos beta+ cos gamma = sin alpha + sin beta + sin gamma = 0 .

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

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)

(sin 5 alpha-sin3alpha)/(cos 5 alpha+2 cos 4 alpha+cos 3alpha)=

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 .