CBSE Class 10 Maths (Standard) 2025 · Paper 30/5/1 · Question 30(a)

Introduction to Trigonometry 3 marks Medium

Prove the following trigonometric identity:

\frac{1 + csc A}{csc A} = \frac{cos ^{2} A}{1 - sin A}

Answer

The left-hand side simplifies to

1 + sin A

, and multiplying and dividing by

1 - sin A

turns this into

\frac{1 - s i n ^{2} A}{1 - s i n A} = \frac{c o s ^{2} A}{1 - s i n A}

, the right-hand side; hence the identity is proved.

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