MHT CET · Maths · Differentiation
If \(x=a \sin 2 t(1+\cos 2 t), y=b \cos 2 t(1-\cos 2 t)\) then \(\frac{d y}{d x}\) is equal to
- A \(\frac{\mathrm{b}}{\mathrm{a}} \tan \mathrm{t}\)
- B \(\frac{a}{b} \tan t\)
- C \(\frac{\mathrm{b}}{a \tan \mathrm{t}}\)
- D \(\frac{a}{b \tan t}\)
Answer & Solution
Correct Answer
(A) \(\frac{\mathrm{b}}{\mathrm{a}} \tan \mathrm{t}\)
Step-by-step Solution
Detailed explanation
\(\frac{dx}{dt} = a \frac{d}{dt} (\sin 2t(1+\cos 2t)) = a [(2 \cos 2t)(1+\cos 2t) + \sin 2t(-2 \sin 2t)] = 2a (\cos 2t + \cos 4t) = 4a \cos 3t \cos t\) \(\frac{dy}{dt} = b \frac{d}{dt} (\cos 2t(1-\cos 2t)) = b [(-2 \sin 2t)(1-\cos 2t) + \cos 2t(2 \sin 2t)] = 2b (-\sin 2t + \sin 4t) = 4b \cos 3t \sin t\)
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