Question

Find the equation of the tangent to the curve y = 2 sin x + sin 2x at x =π/3​

Answer 1

Answer:

please see the attachment

Answer 2

Equation of the tangent will be $\bold{2 y-3 \sqrt{3}=0}$.

Solution:

If $x=\frac{\pi}{3}$, then

$\begin{array}{l}{y=2 \sin \frac{\pi}{3}+\sin \frac{2 \pi}{3}} \\ \\{=\frac{2 \sqrt{3}}{2}+\frac{\sqrt{3}}{2}} \\ \\{=\frac{3 \sqrt{3}}{2}} \\ \\{(x y)=\left(\frac{\pi}{3}, \frac{3 \sqrt{3}}{2}\right)} \\ \\{\frac{d y}{d x}=2 \cos x+(\cos 2 x) 2}\end{array}$

$=2(\cos x+\cos 2 x)$

$\left(\frac{d y}{d x}\right) \frac{\pi}{3}=2\left[\cos \frac{\pi}{3}+\cos \frac{2 \pi}{3}\right]$

$\begin{array}{l}{=2\left[\frac{1}{2}-\frac{1}{2}\right]} \\ \\{=0}\end{array}$

Hence, m = 0

Equation of the tangent will be $\bold{\mathrm{y}-\frac{3 \sqrt{3}}{2}=0 \Rightarrow 2 y-3 \sqrt{3}=0.}$