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Question

If y=tan1cosx+sinxcosxsinx, then find dydx.

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Solution

Given,
y=tan1cosx+sinxcosxsinx

or, y=tan11+tanx1tanx [ Dividing the numerator and the denominator by cosx]

or, y=tan1tanπ4+tanx1tanπ4tanx

or, y=tan1tan(π4x) [ Since tanπ4=1]

or, y=π4+x

So dydx=1.

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