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Question

If y=tan-1 sin x+cos xcos x-sin x, then dydx is equal to
(a) 12
(b) 0
(c) 1
(d) none of these

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Solution

(c) 1

We have, y=tan-1sinx+cosxcosx-sinxdydx=11+sinx+cosxcosx-sinx2ddxsinx+cosxcosx-sinxdydx=cosx-sinx2cosx-sinx2+sinx+cosx2cosx-sinxddxsinx+cosx-sinx+cosxddxcosx-sinxcosx-sinx2dydx=cosx-sinx2cosx-sinx2+sinx+cosx2cosx-sinxcosx-sinx-sinx+cosx-sinx-cosxcosx-sinx2dydx=cosx-sinx2cosx-sinx2+sinx+cosx2cosx-sinxcosx-sinx+sinx+cosxsinx+cosxcosx-sinx2dydx=cosx-sinx2cosx-sinx2+sinx+cosx2×cosx-sinx2+sinx+cosx2cosx-sinx2dydx=1

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