Question

Prove that: 4(cos³ 10° + sin³ 20°) = 3(cos 10° + sin 20°)

Answer 1

Let us consider the LHS

4(cos³ 10° + sin³ 20°)

As we know that, sin 60° = √3/2 = cos 30°

Sin 30° = cos 60° = 1/2

Therefore,

Sin (3×20°) = cos (3×10°)

3sin 20° – 4sin³20° = 4cos³10° – 3cos 10°

(As we know, sin 3θ = 3sin θ – 4sin³ θ and cos 3θ = 4cos³θ – 3cosθ)

Therefore,

4(cos³10° + sin³20°) = 3(sin 20° + cos 10°)

= RHS

Thus proved.