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Question

Let y=tan11cos2xsin2x, then prove that dydx=1.

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Solution

Given,
y=tan11cos2xsin2x

or, y=tan12cos2x2sinx.sinx

or, y=tan1cosxsinx

or, y=tan1tan(π2x)

or, y=π2x
Now differentiating both sides with respect to x we get,
dydx=1.

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