Question

Prove that sin60degree= (2tan30degree)/(1+tan^2 30degree)

Answer 1

Solution

L.H.S → sin 60°

R.H.S → 2 tan 30°/(1 + tan² 30°)

• tan 30° = 1/√3
• sin 60° = √3/2

→ (2 × 1/√3)/(1 + 1/√3²)

→ (2/√3)/(1 + 1/3)

(っ.❛ ᴗ ❛.)っ

On rationalizing 2/√3 we get

→ 2/√3 × √3/√3 = 2√3/3

→ 2√3/3 ÷ 4/3

→ 2√3/3 × 3/4

→ √3/2 = sin 60° = L.H.S

Q.E.D