CBSE Class 10 Mathematics Basic 2023: question 27

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

   1 mark

2. $=\frac{\frac{{\cos }^{2}A+{\sin }^{2}A}{{\cos }^{2}A}}{\frac{{\sin }^{2}A+{\cos }^{2}A}{{\sin }^{2}A}}$

   ½ mark

3. $=\frac{\frac{1}{{\cos }^{2}A}}{\frac{1}{{\sin }^{2}A}}=\frac{{\sin }^{2}A}{{\cos }^{2}A}=\frac{1-{\cos }^{2}A}{{\cos }^{2}A}$ [using ${\sin }^{2}A+{\cos }^{2}A=1$]

   1 mark

4. $=\frac{1}{{\cos }^{2}A}-1={\sec }^{2}A-1=$ RHS

   ½ mark

Answer: LHS = sec²A − 1 = RHS (proved)

Revise the chapter

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