SOLUTION: prove that cosAcos(60-A)cos(60+A)=1/4cos3A.
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Question 710571: prove that cosAcos(60-A)cos(60+A)=1/4cos3A.
Answer by srinivas.g(540) (Show Source): You can put this solution on YOUR website!
formula for cox( x+y) cos(x-y) = cos ^2 (y) - sin^2( x)
here cos (60-A) cos (60+A) = cos^2(A)- sin^2 (60)
= cos ^2 (A) - 3/4
now cos A cos (60-A) cos (60+A = cos A ( cos^2 (A) - 3/4)
\ = 1/4 ( 4 cos ^3 (a) - 3 cos A)
{since 4 cos ^3 (a) - 3 cos A = cos 3A }
= 1/4 ( cos 3A)
hence proved
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