CBSE Class 10 Mathematics Basic 2024: question 31(a)

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 $={\sin }^2\theta +{\text{cosec}}^2\theta +2\sin \theta \text{cosec}\theta +{\cos }^2\theta +{\sec }^2\theta +2\cos \theta \sec \theta$

   1 mark

2. $=({\sin }^2\theta +{\cos }^2\theta )+{\text{cosec}}^2\theta +{\sec }^2\theta +2\sin \theta \cdot \frac{1}{\sin \theta }+2\cos \theta \cdot \frac{1}{\cos \theta }$

   ½ mark

3. Using ${\sin }^2\theta +{\cos }^2\theta =1$, ${\text{cosec}}^2\theta =1+{\cot }^2\theta$, ${\sec }^2\theta =1+{\tan }^2\theta$:
   $=1+(1+{\cot }^2\theta )+(1+{\tan }^2\theta )+2+2$

   1 mark

4. $=7+{\tan }^2\theta +{\cot }^2\theta =$ RHS. Hence proved.

   ½ mark

Answer: LHS simplifies to $7+{\tan }^2\theta +{\cot }^2\theta$ = RHS; proved.

Revise the chapter

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