Q16 of 123 Page 9

Prove the following identities:

Proof:

Take LHS:

Identities used:

cos² A – sin² A = cos 2A

Therefore,

= RHS

Hence Proved

Prove the following identities:

cos³ 2x + 3 cos 2x = 4(cos⁶ x – sin⁶ x)

Prove the following identities:

(sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0

Prove the following identities:

cos 4x = 1 – 8 cos² x + 8 cos⁴ x

Prove the following identities:

sin 4x = 4 sin x cos³ x – 4 cos x sin³ x