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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 5 · Set 1 · Q29
Prove that: (tan A)/(1- cot A)+(cot A)/(1- tan A)=1+ sec A cosec A
Prove that : \[\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}=1+\sec A \operatorname{cosec} A \]
Marking-scheme solution
\[\begin{aligned}
\mathrm{LHS} & =\frac{\dfrac{\sin A}{\cos A}}{\dfrac{(\sin A-\cos A)}{\sin A}}+\frac{\dfrac{\cos A}{\sin A}}{\dfrac{(\cos A-\sin A)}{\cos A}} \\
& =\frac{1}{(\sin A-\cos A)}\left[\frac{\sin ^{2} A}{\cos A}-\frac{\cos ^{2} A}{\sin A}\right] \\
& =\frac{1}{(\sin A-\cos A)} \times \frac{(\sin A-\cos A)\left(\sin ^{2} A+\cos ^{2} A+\sin A \cos A\right)}{\sin A \cos A} \\
& =\frac{1}{\sin A \cos A}+1 \\
& =1+\sec A \operatorname{cosec} A=\mathrm{RHS}
\end{aligned}
\]
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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.