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Mathematics · 2023 · 3 marks
CBSE 2023 · Region 6 · Set 3 · Q26
Prove that ( sin θ+ cos θ)( tan θ+ cot θ)= sec θ+ cosec θ.
Prove that $\displaystyle (\sin \theta+\cos \theta)(\tan \theta+\cot \theta)=\sec \theta+\operatorname{cosec} \theta$.
Marking-scheme solution
\[\begin{aligned}
\text { LHS }=(\sin \theta+\cos \theta) & \left(\frac{\sin \theta}{\cos \theta}+\frac{\cos \theta}{\sin \theta}\right) \\
& =(\sin \theta+\cos \theta)\left(\frac{\sin ^{2} \theta+\cos ^{2} \theta}{\cos \theta \sin \theta}\right) \\
& =\frac{(\sin \theta+\cos \theta) \cdot(1)}{\cos \theta \sin \theta} \\
& =\sec \theta+\operatorname{cosec} \theta=\mathrm{RHS}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.