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Question

If x = 2 cos t – cot 2t, y = 2 sin t – sin 2t, then d2ydx2 at t=π2

A
52
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B
32
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C
32
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D
52
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Solution

The correct option is B 32
dydx=dydtdxdt=2cost2cos2t2sint2sin2t=costcos2tsin2tsint=2sin(3t2)sint22cos(3t2)sint2=tan(3t2)d2ydx2=ddx(dydx)=ddx(tan3t2)=ddttan(3t2).dtdx=32.sec2(3t2).1(2sint+2sin2t)d2ydx2|t=π2=32sec2(3π4).1(2+0)=34(2)2=32

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