Question

Prove the identity.
6cos^2(x)-1 -12cos^4(x) +8cos^6(x)= cos^3(2x)

Thanks for your help :)

Answer 1

Use the fact that
cos(2x) = 2 cos^2 x - 1

The left side of your identity is
(2 cos^2x -1)^3
Let's prove that:
= (4 cos^4x -4 cos^2x +1)(2 cos^2x -1)
= 8 cos^6x -12 cos^4x +6 cos^2 -1
Therefore
8 cos^6x -12 cos^4x +6 cos^2 -1
= cos^3(2x)

Answer 2

Thank you for your help :)
By the way, i wanna ask which side i should start when i am asked to prove this boring identities and which formulae i should use. There r so many formulaes !!!! You know, i just dun have the "sense of mathematics". My friends can do this sum in 5 mins. I just cant figure how how he can do it.

Answer 3

You can start on either side. It all depends upon which side already looks uncomplicated. Try simplifying the other side first. There is no single formula to use. Knowing the double angle formulas and the definitions if tan, cot, sec and csc in therms of sin and cos almost always helps.