Question

1- sin theta/1+sin theta =( sec theta - tan theta)​

Answer 1

Correct Question

Prove (1 - sin∅)/(1 + sin∅) = (sec∅ - tan∅)².

Solution

L.H.S → (1 - sin∅)/(1 + sin∅)

On multiplying by (1 - sin∅),

→ (1 - sin∅)/(1 + sin∅) × (1 - sin∅)/(1 - sin∅)

→ (1 - sin∅)²/(1 - sin²∅)

→ (1 - sin∅)²/cos²∅

→ [(1 - sin∅)/cos∅]²

→ [1/cos∅ - sin∅/cos∅]²

• sec∅ = 1/cos∅
• sin∅/cos∅ = tan∅

→ [sec∅ - tan∅]² = R.H.S

Hence Proved