CBSE Class 10 Mathematics Standard 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 $=\left(\frac{1-{\cos }^2\theta }{\cos \theta }\right)\left(\frac{1-{\sin }^2\theta }{\sin \theta }\right)$

   ½ mark

2. $=\frac{{\sin }^2\theta }{\cos \theta }\times \frac{{\cos }^2\theta }{\sin \theta }=\sin \theta \cos \theta$ [using ${\sin }^2\theta +{\cos }^2\theta =1$]

   1 mark

3. RHS $=\frac{1}{\frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta }}$

   ½ mark

4. $=\frac{\sin \theta \cos \theta }{{\sin }^2\theta +{\cos }^2\theta }=\sin \theta \cos \theta$
   Therefore LHS = RHS. Hence proved.

   1 mark

Answer: Both sides equal $\sin \theta \cos \theta$; hence proved.

Revise the chapter

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