Question

Equation of the tangent at $x=\frac{\pi }{2}$ to curve $y=x\sin x$ is -

• A. $x+y=0$
• B. $x-y=0$
• C. $x+y=\pi$
• D. $x-y=\pi$

Answer 1

The correct option is B $x-y=0$

$\frac{dy}{dx}{|}_{(\frac{\pi }{2},\frac{\pi }{2})}=1$, So the equation of the tangent

$y-\frac{\pi }{2}=x-\frac{\pi }{2}\Rightarrow x-y=0$