CBSE Class 10 Mathematics Standard 2025: question 29(B)

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 $=p^2-q^2=(p+q)(p-q)=[(\cot \theta +\cos \theta )+(\cot \theta -\cos \theta )][(\cot \theta +\cos \theta )-(\cot \theta -\cos \theta )]$

   1 mark

2. $=2\cot \theta \times 2\cos \theta =4\cot \theta \cos \theta$

   ½ mark

3. RHS $=4\sqrt{(\cot \theta +\cos \theta )(\cot \theta -\cos \theta )}=4\sqrt{{\cot }^2\theta -{\cos }^2\theta }$

   ½ mark

4. $=4\sqrt{\frac{{\cos }^2\theta }{{\sin }^2\theta }-{\cos }^2\theta }=4\sqrt{{\cos }^2\theta ({\mathrm{cosec}}^2\theta -1)}$

   ½ mark

5. $=4\sqrt{{\cos }^2\theta {\cot }^2\theta }=4\cot \theta \cos \theta$. Hence LHS = RHS.

   ½ mark

Answer: $p^2-q^2=4\cot \theta \cos \theta =4\sqrt{pq}$ (proved)

Revise the chapter

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