Question

The equation of the tangent to the curve $y=2\sin x+\sin 2x$ at $x=\frac{\pi }{3}$ on it is

• A. $y-3=0$
• B. $y+\sqrt{3}=0$
• C. $2y-3=0$
• D. $2y-3\sqrt{3}=0$

Answer 1

The correct option is D $2y-3\sqrt{3}=0$

$x=\frac{\pi }{3}\Rightarrow y=2\left(\frac{\sqrt{3}}{2}\right)+\frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{2}$

$y^1=2\cos x+2\cos 2x$

at $x=\frac{\pi }{3}\Rightarrow y^1=2\left(\frac{1}{2}\right)+2\left(\frac{-1}{2}\right)$

$=0$

$\therefore$ equation of tangent is

$\frac{y-3\sqrt{3}/2}{x=\pi /3}=0$

$\Rightarrow y=\frac{3\sqrt{3}}{2}$