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Question

If y=x+tanx, prove that cos2xd2ydx2+2x=2y

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Solution

Given y=x+tanx

Differentiate with respect to x we get

dydx=1+sec2x

Again differentiate with respect to x we get

d2ydx2=0+2secx(secxtanx)

d2ydx2=2sec2xtanx

1sec2xd2ydx2=2tanx

cos2xd2ydx2=2(yx)

cos2xd2ydx2=2y2x

cos2xd2ydx2+2x=2y

Hence proved.

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