CBSE Class 10 Mathematics Standard sample paper 2025-26: question 29(A)

Hints

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Step-by-step solution

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1. Squaring both sides: $(\sin \theta +\cos \theta {)}^2=3$, so ${\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta =3$, which gives $1+2\sin \theta \cos \theta =3$.

   1 mark

2. So $2\sin \theta \cos \theta =2$, i.e. $\sin \theta \cos \theta =1$.

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3. $\tan \theta +\cot \theta =\frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta }=\frac{{\sin }^2\theta +{\cos }^2\theta }{\sin \theta \cos \theta }=\frac{1}{\sin \theta \cos \theta }=\frac{1}{1}=1$. Hence proved.

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Answer: tan θ + cot θ = 1 (proved)

Revise the chapter

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