Question 735965
 cos(4θ) = 
cos(2*(2θ)) = 
2cos^2(2θ) - 1 = 
 2[ 2cos^2(θ) - 1 ]^2 - 1
 2 [ 4cos^4(θ) - 4cos^2(θ) + 1 ] - 1
 8cos^4(θ) - 8cos^2(θ) + 1.....................(1)

.............

4 cos 2theta

4(2 cos^2{{{ Theta}}}-1)

8 cos^2{{{ theta}}}-4................................(2)

(1)+(2)= RHS


8cos^4(θ) - 8cos^2(θ) + 1  + 8 cos^2{{{ theta}}}-4= RHS