# For x belongs to(0,180),the equation sinx+2sin2x−sin3x=3 has how many solutions?

Sourabh Singh IIT Patna
6 years ago
Hii

Use the combination of sinx−sin3x to write it into format of sin2x . You will get the values of it in terms of product from where you can find out the answer
jagdish singh singh
173 Points
6 years ago
$\hspace{-0.6 cm}Write as (\sin 2x-1)^2+(\cos 2x+\sin x)^2+(\cos x)^2=0\; \forall x\in (0,\pi)\\\\ So either \sin 2x = 1 and \cos 2x = -\sin x and \cos x=0\\\\ So from above no common value of x\in (0,\pi)\\\\ for which above equation is satisfied.\\\\ So no real values of x$