Q) Prove that : √[(1 + sin A)/(1−sin A)] = sec A + tan A.

(Q 25 A – 30/4/2 – CBSE 2026 Question Paper)

Ans:

Step 1: Let’s start solving LHS:

LHS =

Here we have (1 – sin A) in the denominator.

To nullify this, we need to multiply & divide by its conjugate i.e. (1 + sin A):

∴ LHS =

=

Step 2: By algebraic identity, (a – b) (a + b) = a ² – b ²

∴ LHS =

=

Step 3: ∵ by trigonometric identity, sin ² θ + cos ² θ = 1

∴ 1 – sin ² θ = cos ² θ

∴ LHS =

=

=

=

=

= sec A + tan A

= RHS ………. Hence Proved !

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