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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 5 · Set 1 · Q26
(a) Find dy/dx, if ( cos x )^y =( cos y )^x.
(a)
Find $\displaystyle \frac{\mathrm{dy}}{\mathrm{dx}}$, if $\displaystyle (\cos \mathrm{x})^{\mathrm{y}}=(\cos \mathrm{y})^{\mathrm{x}}$.
OR
(b)
If $\displaystyle \sqrt{1-\mathrm{x}^{2}}+\sqrt{1-\mathrm{y}^{2}}=a(\mathrm{x}-\mathrm{y})$, prove that $\displaystyle \frac{d \mathrm{y}}{d \mathrm{x}}=\sqrt{\frac{1-\mathrm{y}^{2}}{1-\mathrm{x}^{2}}}$.
Marking-scheme solution
(a)
Taking 'log' on both sides of $\displaystyle (\cos \mathrm{x})^{\boldsymbol{\mathrm{y}}} \boldsymbol{=}(\cos \mathrm{y})^{\boldsymbol{\mathrm{x}}}$, we get $\displaystyle \mathrm{y} \log \cos \mathrm{x}=\mathrm{x} \log \cos \mathrm{y}$
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CBSE Class 12 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.