Q11 of 118 Page 5

Prove the following identities
= sinx cosx

LHS

We know that

We know that a³ + b³ = (a + b) (a² + b²- ab)

= 1 – (sin²x + cos²x) + sinx cosx

We know that sin²x + cos²x = 1.

= 1 – 1 + sinx cosx

= sinx cosx

= RHS

Hence proved.

Prove the following identities

sin²x cos²x

Prove the following identities

(1 + tan α tan β)² + (tan α – tan β)² = sec² α sec² β