CBSE Class 10 Mathematics Basic 2026: question 29

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 $=\sqrt{\frac{1-\sin A}{1+\sin A}\times \frac{1-\sin A}{1-\sin A}}=\sqrt{\frac{(1-\sin A{)}^2}{1-{\sin }^{2}A}}=\sqrt{\frac{(1-\sin A{)}^2}{{\cos }^{2}A}}=\frac{1-\sin A}{\cos A}$

   1 mark

2. $=\frac{1}{\cos A}-\frac{\sin A}{\cos A}=\sec A-\tan A$

   ½ mark

3. $=(\sec A-\tan A)\times \frac{\sec A+\tan A}{\sec A+\tan A}$

   ½ mark

4. $=\frac{{\sec }^{2}A-{\tan }^{2}A}{\sec A+\tan A}$

   ½ mark

5. $=\frac{1}{\sec A+\tan A}$ [${\sec }^{2}A-{\tan }^{2}A=1$] $=$ RHS. Hence proved.

   ½ mark

Answer: LHS = $\sec A-\tan A=\frac{1}{\sec A+\tan A}$ = RHS (proved)

Revise the chapter

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