Q16 of 186 Page 332

Prove each of the following identities:

Consider L.H.S. =

= sin θ (cos³ θ) + cos θ (sin³ θ)

= sin θ cos θ (cos² θ + sin² θ)

= sin θ cos θ

= R.H.S.

Hence, proved.

Prove each of the following identities:

sin⁶ θ + cos⁶ θ = 1 – 3 sin² θ cos² θ

Prove each of the following identities:

sin² θ + cos⁴θ = cos² θ + sin⁴ θ