Find general solution of the equation?

**fardeen_gen** · April 30th 2009, 08:34 PM

Find general solution of the equation:
$\sin \frac{2x + 1}{x} + \sin \frac{2x + 1}{3x} - 3\cos^2 \frac{2x + 1}{3x} = 0$

Answer:

Spoiler:

I am unable to solve it. Anyone?

**red_dog** · April 30th 2009, 11:17 PM

Use $\sin a+\sin b=2\sin\frac{a+b}{2}\cos\frac{a-b}{2}$

$2\sin 2\left(\frac{2x+1}{3x}\right)\cos\frac{2x+1}{3x}-3\cos^2\frac{2x+1}{3x}=0$

Now use $\sin 2a=2\sin a\cos a$

$2\sin\frac{2x+1}{3x}\cos^2\frac{2x+1}{3x}-3\cos^2\frac{2x+1}{3x}=0$

$\cos^2\frac{2x+1}{3x}\left(2\sin\frac{2x+1}{3x}-3\right)=0$

Then, $\cos\frac{2x+1}{3x}=0\Rightarrow\frac{2x+1}{3x}=(2 k+1)\frac{\pi}{2}$ and find x.

If $2\sin\frac{2x+1}{3x}-3=0\Rightarrow\sin\frac{2x+1}{3x}=\frac{3}{2}>1$ and it has no solution.

Thread: Find general solution of the equation?

LinkBack

Thread Tools

Display

Find general solution of the equation?

Similar Math Help Forum Discussions

Find the general solution to the equation 2u_x + u_xy = 0

Find the general solution of the differential equation specified..

Find General Solution?

find the general solution when 1 solution is given

Find the general solution for the differential equation

Search Tags