CBSE Class 10 Mathematics Standard 2026: question 28(b)

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. LHS $=(p^2-q^2){\sec }^2\alpha =\left(\frac{{\sec }^2\alpha }{{\mathrm{cosec}}^2\beta }-\frac{{\tan }^2\alpha }{{\mathrm{cosec}}^2\beta }\right){\sec }^2\alpha$

   ½ mark

2. $=\left(\frac{{\sec }^2\alpha -{\tan }^2\alpha }{{\mathrm{cosec}}^2\beta }\right){\sec }^2\alpha$

   1 mark

3. $=\frac{1}{{\mathrm{cosec}}^2\beta }\times {\sec }^2\alpha$ [since ${\sec }^2\alpha -{\tan }^2\alpha =1$]

   1 mark

4. $=\frac{{\sec }^2\alpha }{{\mathrm{cosec}}^2\beta }=p^2=$ RHS

   ½ mark

Answer: Proved: $(p^2-q^2){\sec }^2\alpha =p^2$

Revise the chapter

• Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)
• Topic: Proving Simple Trigonometric Identities