The number of values of x in the interval [0, | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(c) $3{\sin ^2}x - 7\sin x + 2 = 0$

$ \Rightarrow $ $3{\sin ^2}x - 6\sin x - \sin x + 2 = 0$

$ \Rightarrow $ $3\sin (\sin x - 2) - (\sin x - 2)

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(c) $3{\sin ^2}x - 7\sin x + 2 = 0$

$ \Rightarrow $ $3{\sin ^2}x - 6\sin x - \sin x + 2 = 0$

$ \Rightarrow $ $3\sin (\sin x - 2) - (\sin x - 2) = 0$

$ \Rightarrow $ $(3\sin x - 1)\,(\sin x - 2) = 0$

$ \Rightarrow $ $\sin x = \frac{1}{3}{m{ or 2}}$

$ \Rightarrow $ $\sin x = \frac{1}{3}$, ($ \because \,\,\sin x 
e 2$)

Let ${\sin ^{ - 1}}\frac{1}{3} = \alpha $,

$0 < \alpha < \frac{\pi }{2}$ are the solutions in $[0,{m{ }}5\pi ]$. 

Then $\alpha ,$$\pi - \alpha ,\,$$2\pi + \alpha ,$ $\,3\pi - \alpha ,$ $\,4\pi + \alpha $, $5\pi - \alpha $ are the solutions in $[0,\,5\pi ]$.

$	herefore $ Required number of solutions $= 6$.

The number of values of $x$ in the interval $[0, 5 \pi ] $ satisfying the equation $3{\sin ^2}x - 7\sin x + 2 = 0$ is

Similar Questions

The number of distinct solutions of the equation $\frac{5}{4} \cos ^2 2 x+\cos ^4 x+\sin ^4 x+\cos ^6 x+\sin ^6 x=2$ in the interval $[0,2 \pi]$ is

If the solution of the equation $\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right), \quad$ is $\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)$, where $\alpha, \beta$ are integers, then $\alpha+\beta$ is equal to:

The solution of the equation $cos^2\theta\, +\, sin\theta\, + 1\, =\, 0$ lies in the interval

If $A + B + C = \pi$ & $sin\, \left( {A\,\, + \,\,\frac{C}{2}} \right) = k \,sin,\frac{C}{2}$ then $tan\, \frac{A}{2} \,tan \, \frac{B}{2}=$

Values of $\theta (0 < \theta < {360^o})$ satisfying ${\rm{cosec}}\theta + 2 = 0$ are