`cos3 5^(@)+cos8 5^(@)+cos15 5^(@)=`

The value of (cos ^(6)5^(@)-15 cos ^(4) 5^(@) sin ^(2)5^(@)+15 cos ^(2)5^(@)sin ^(4) 5^(@)-sin ^(6)5^(@)) is equal to-

cos^(-1) (cos 8pi/5)

Prove that cos 48^(@) . Cos 12^(@) =(3+sqrt5)/(8) .

cos ^(4) (pi)/(8)+cos ^(4) (3 pi)/(8)+cos ^(4) (5 pi)/(8)+cos ^(4) (7 pi)/(8)=

(1 + cos ((pi) / (8))) (1 + cos (3 (pi) / (8))) (1 + cos (5 (pi) / (8))) (1 + cos (7 (pi) / (8))) =

cos^2(pi/8) +cos^2((3pi)/8) +cos^2((5pi)/8)+cos^2 ((7pi)/8)=2