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

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

Grade:11

2 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
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 $x$

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