CBSE Class 10 Mathematics Standard 2026: question 26(a)

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. Given $\sin \theta +\cos \theta =\sqrt{3}$. Squaring both sides:
   $(\sin \theta +\cos \theta {)}^2=3$

   ½ mark

2. ${\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta =3$
   $\Rightarrow 1+2\sin \theta \cos \theta =3$ [since ${\sin }^2\theta +{\cos }^2\theta =1$]
   $\Rightarrow \sin \theta \cos \theta =1\text{...(i)}$

   1 mark

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

   1 mark

4. Using (i): $\frac{1}{\sin \theta \cos \theta }=\frac{1}{1}=1=$ RHS.
   Hence proved.

   ½ mark

Answer: Shown: $\sin \theta \cos \theta =1$, so $\tan \theta +\cot \theta =\frac{1}{\sin \theta \cos \theta }=1$.

Revise the chapter

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