Mathematics

Mathematics

Problem

For

0<x<\dfrac{\pi}{2}

, a curve is defined by

y=x\sin x\tan x

. (i) Find

\dfrac{dy}{dx}

and simplify your answer as far as possible. (ii) Determine the value of

\dfrac{dy}{dx}

at

x=\dfrac{\pi}{4}

. (iii) Using your result from part (ii), find the acute angle made by the tangent to the curve with the positive direction of the

x

-axis at the point where

x=\dfrac{\pi}{4}

.

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