InterviewSolution
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InterviewSolution
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If ` x = 2 cos t - cos 2t , y = 2 sin t - sin 2t`, then the value of ` |(d^(2) y)/(dx^(2))|_(t= pi//2 ) `isA. `3//2`B. `5//2`C. `5//2`D. `-3//2` |
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Answer» Correct Answer - D `(dx)/(dt)=2cost-2 cos 2t` `therefore (dy)/(dx)=(2 cos t-2 cos 2t)/(-2 sin t+2sin 2t)` `=(cos -cos 2t)/(-2sin 2t-sin t)` `=(cos t-cos 2t)/(sin 2t-sin t)` `implies(2 sin""(3t)/(2)*sin""(t)/(2))/(2cos ""(3t)/(2)*sin ""(t)/(2))` `=tan ""(3t)/(2)` `(d^(2)y)/(dx^(2))=sec ^(2)""(3t)/(2)*3/2*(dt)/(dx)` `=3/2sec^(2)""(3t)/(2)(1)/((2 sin 2t-2sin t))` `implies(d^(2)y)/(dx^(2))|_(t=pi//2)=-3//2` |
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