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If y = b sin3t and x = a cos3t, then find the value of \(\rm dy \over dx\)
1.  - \(b\over a\) tan t
2. \(b\over a\)tan t
3. \(a \over b\) cot t
4. - \(a \over b\)cot t

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Correct Answer - Option 1 :  - \(b\over a\) tan t

Concept:

\(\rm d(sinx) \over dt\) = cosx

\(\rm d(cosx) \over dt\)= -sinx

\(\rm sinx \over cosx\)= tanx

 

Calculation:

Given,

y =  b sin3t

\(\rm dy \over dt\)= 3 b sin2t cos t          ....(1)

Similarly,

x = a cos3t

\(\rm dx \over dt\) = 3 a cos2t (-sin t)      ....(2)

Dividing eq(1) by eq(2) we get,

\(\rm \frac{\frac{dy}{dt}}{\frac{dx}{dt}}\)\(\rm 3 b \sin^2 t \cos t \over -3 a \cos^2 t \sin t\)

\(\rm dy\over dx\) = \(\rm -b \over a \)tan t

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