CBSE Class 10 Mathematics Standard 2025: question 28(a)

Hints

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Step-by-step solution

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1. Write both terms over the common denominator $\sqrt{(\sec A+1)(\sec A-1)}$:

   $\text{LHS}=\frac{(\sec A-1)+(\sec A+1)}{\sqrt{(\sec A+1)(\sec A-1)}}=\frac{2\sec A}{\sqrt{{\sec }^{2}A-1}}$

   1 mark

2. Since ${\sec }^{2}A-1={\tan }^{2}A$:

   $\text{LHS}=\frac{2\sec A}{\tan A}$

   1 mark

3. $=\frac{2}{\cos A}\times \frac{\cos A}{\sin A}=\frac{2}{\sin A}=2\mathrm{cosec}A=\text{RHS}$

   1 mark

Answer: LHS = $2\mathrm{cosec}A$ = RHS. Hence proved.

Revise the chapter

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