Question

Write the differential coefficient of tan^-1(sin x + cos x/cos x-sin x) with respect to x
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Answer 1

Answer:

$y = arc \tan( \frac{ \sin(x) + \cos(x) }{ \cos(x) - \sin(x) } ) \\ divding \: both \: numerator \: and \: denomiator \: by \: \cos(x) \\ then \: y =arc \tan( \frac{1 + \tan(x) }{1 - \tan(x) } ) \\ \\ y = arc \tan( \tan( \frac{\pi}{4} + x) ) \\ y = \frac{\pi}{4} + x \\ therefore \: \frac{dy}{dx} = 0 + 1 = 1$

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