If `alpha = pi/3`, prove that `cos alpha . Cos 2alpha . Cos 3alpha . Cos 4alpha . Cos 5alpha cos 6alpha = 1/16`.

cos alpha cos 2 alpha cos 4 alpha cos 8 alpha = (1)/(16), if alpha = 24 ^(@)

(cos alpha + 2 cos 3 alpha + cos 5 alpha )/(cos 3 alpha + 2 cos 5 alpha + cos 7 alpha ) = cos 3 alpha sec 5 alpha .

If alpha+beta= 60^0 , prove that cos^2 alpha + cos^2 beta - cosalpha cos beta = 3/4 .

cos2 alpha-cos3alpha-cos4alpha+cos5alpha simplifies to :

In Delta ABC , prove that c cos (A - alpha) + a cos (C + alpha) = b cos alpha

(cos ^(3) alpha - cos 3 alpha )/( cos alpha ) + (sin ^(3)alpha + sin 3 alpha )/( sin alpha ) = 3.

Evaluate cos alpha cos 2 alpha cos 3 alpha..........cos 999alpha , where alpha=(2pi)/(1999)

Prove by using principle of induction that: cos alpha+cos 2alpha+…+cos n alpha = sin. (nalpha)/2 cosec alpha/2 cos. ((n+1)alpha)/2

Express cos 6 alpha in terms of cos 3 alpha .

1/(cosalpha+cos3alpha)+1/(cosalpha+cos5alpha)....1/(cosalpha+cos(2n+1)alpha