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Mathematics · 2023 · 3 marks
CBSE 2023 · Region 1 · Set 1 · Q30
Prove that: (tan θ+ sec θ-1)/(tan θ- sec θ+1)=(1+ sin θ)/(cos θ)
Prove that : $\displaystyle \frac{\tan \theta+\sec \theta-1}{\tan \theta-\sec \theta+1}=\frac{1+\sin \theta}{\cos \theta}$
Marking-scheme solution
\[\begin{aligned}
\mathrm{LHS} & =\frac{(\tan \theta+\sec \theta)-\left(\sec ^{2} \theta-\tan ^{2} \theta\right)}{\tan \theta-\sec \theta+1} \\
& =\frac{(\tan \theta+\sec \theta)(1-\sec \theta+\tan \theta)}{\tan \theta-\sec \theta+1} \\
& =\tan \theta+\sec \theta \\
= & \frac{1+\sin \theta}{\cos \theta}=\mathrm{RHS}
\end{aligned}
\]
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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.