CBSE Class 10 Mathematics Basic 2025: question 30

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 $=\frac{\cos \theta }{1+\sin \theta }+\frac{1+\sin \theta }{\cos \theta }=\frac{{\cos }^2\theta +(1+\sin \theta {)}^2}{(1+\sin \theta )\cos \theta }$

   1 mark

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

   ½ mark

3. Using ${\sin }^2\theta +{\cos }^2\theta =1$: $=\frac{2+2\sin \theta }{(1+\sin \theta )\cos \theta }=\frac{2(1+\sin \theta )}{(1+\sin \theta )\cos \theta }$

   1 mark

4. $=\frac{2}{\cos \theta }=2\sec \theta =$ RHS. Hence proved.

   ½ mark

Answer: LHS simplifies to 2 sec θ = RHS

Revise the chapter

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