CBSE Class 10 Mathematics Basic 2026: question 30

Hints

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

   1 mark

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

   1 mark

3. $=\frac{2(1+\sin \theta )}{(1+\sin \theta )\cos \theta }=\frac{2}{\cos \theta }=2\sec \theta =$ RHS. Hence proved.

   1 mark

Answer: LHS simplifies to $2\sec \theta$ = RHS

Revise the chapter

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