Question

show that : [sec theta - tan theta]² =1-sin theta divided by 1+ sin theta

Answer 1

Answer:

Step-by-step explanation:

Given, [secθ - tanθ]² = (1 - sinθ) / (1 + sinθ)

L.H.S = [secθ - tanθ]²

⇒ sec²θ + tan²θ - 2secθtanθ

⇒ (1 / cos²θ) + (sin²θ / cos²θ) - (2sinθ / cos²θ)

⇒ (sin²θ - 2sinθ + 1) / cos²θ  

⇒ (1 - sinθ)² / (1 - sin²θ)

⇒ [(1 - sinθ)(1 - sinθ)] / [(1 + sinθ)(1 - sinθ)]

⇒ (1 - sinθ) / (1 + sinθ) = R.H.S

Hence, proved

Hope it helps!!