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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 5 · Set 2 · Q30
Prove that: (sin θ)/(1+ cos θ)+(1+ cos θ)/(sin θ)=2 cosec θ
Prove that : \[\frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}=2 \operatorname{cosec} \theta \]
Marking-scheme solution
\[\begin{aligned}
\mathrm{LHS} & =\frac{\sin ^{2} \theta+1+\cos ^{2} \theta+2 \cos \theta}{\sin \theta(1+\cos \theta)} \\
& =\frac{2+2 \cos \theta}{\sin \theta(1+\cos \theta)} \\
& =\frac{2}{\sin \theta} \\
& =2 \operatorname{cosec} \theta=\mathrm{RHS}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.