Question

Prove that

8cos³ 20° - 6cos20° = 1

Answer 1

To Prove: 8 cos³ 20° - 6 cos 20° = 1

Taking LHS,

= 8 cos³ 20° - 6 cos 20°

Taking 2 common, we get

= 2(4 cos³ 20° - 3 cos 20°) …(i)

We know that,

cos 3x = 4cos³x – 3 cosx

Here, x = 20°

So, eq. (i) becomes

= 2[cos 3(20°)]

= 2[cos 60°]

= 1

= RHS

∴ LHS = RHS

Hence Proved