Q) Prove that: √(1 – sin θ)/(1 + sin θ) = sec θ – tan θ.

(Q 24 B – 30/2/1 – CBSE 2026 Question Paper)

Ans: 

Let’s start from LHS:

LHS =

Step 1: [Note: Since in RHS, we need to get cos θ in denominator, hence, we need to nullify + sign]

∴ Let’s both multiply & divide the expression by (1 – sin θ)

LHS =

∴ LHS =

=             (∵ (a + b)(a – b) = a ² + b ²)

Step 2: ∵ we know that sin ² θ + cos ² θ = 1

∴ cos ² θ = 1 – sin ² θ

∴ LHS =

=

=

= sec θ – tan θ = RHS

Hence Proved !

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