CBSE Class 10 Mathematics Standard 2025: question 24(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. Expand: ${\sin }^{2}A+{\mathrm{cosec}}^{2}A+2\sin A\mathrm{cosec}A+{\cos }^{2}A+{\sec }^{2}A+2\cos A\sec A$
   $={\sin }^{2}A+{\mathrm{cosec}}^{2}A+2+{\cos }^{2}A+{\sec }^{2}A+2$

   ½ mark

2. Use ${\sin }^{2}A+{\cos }^{2}A=1$, ${\mathrm{cosec}}^{2}A=1+{\cot }^{2}A$, ${\sec }^{2}A=1+{\tan }^{2}A$:
   LHS $=1+4+(1+{\cot }^{2}A)+(1+{\tan }^{2}A)=7+{\tan }^{2}A+{\cot }^{2}A$

   1 mark

3. Comparing with $x+{\tan }^{2}A+{\cot }^{2}A$: $x=7$.

   ½ mark

Answer: $x=7$

Revise the chapter

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