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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 3 · Set 2 · Q27
Prove that (sin A + cos A)/(sin A - cos A)+(sin A - cos A)/(sin A + cos A)=2/(2 sin^2 A -1)
Prove that $\displaystyle \frac{\sin \mathrm{A}+\cos \mathrm{A}}{\sin \mathrm{A}-\cos \mathrm{A}}+\frac{\sin \mathrm{A}-\cos \mathrm{A}}{\sin \mathrm{A}+\cos \mathrm{A}}=\frac{2}{2 \sin ^{2} \mathrm{~A}-1}$
Marking-scheme solution
\[\begin{aligned}
\text { L.H.S } & =\frac{(\sin A+\cos A)^{2}+(\sin A-\cos A)^{2}}{(\sin A-\cos A)(\sin A+\cos A)} \\
& =\frac{\sin ^{2} A+\cos ^{2} A+2 \sin A \cos A+\sin ^{2} A+\cos ^{2} A-2 \sin A \cos A}{\sin ^{2} A-\cos ^{2} A} \\
& =\frac{1+1}{\sin ^{2} A-\left(1-\sin ^{2} A\right)} \\
& =\frac{2}{2 \sin ^{2} A-1}=\text { R.H.S. }
\end{aligned}
\]
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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.