Q) Prove the following trigonometric identity: (1 + cosec A) / (cosec A) = (cos² A) / (1 – sin A)

PYQ: 30 (a) – CBSE 2025 – Code 30 – Series 5 – Set 1

Ans: Let’s start from LHS

LHS = (1 + cosec A) / (cosec A)

= (1 + (1 / sin A)) / (1 / sin A)

= ((sin A + 1) / sin A) / (1 / sin A)

= ( 1 + sin A) / 1

Let’s multiply by (1- sin A) in the numerator and denominator both:

∴ LHS = (1 + sin A) (1 – sin A) / 1 (1 – sin A)

= (1 – sin² A) / (1 – sin A)

= cos² A / (1 – sin A)

= RHS ……….. Hence, proved !

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