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Question

Question: The number of solutions of the equation \(3\sin^{2}x - 7\sin x + 2 = 0\)in the interval \(\lbrack 0,...

The number of solutions of the equation 3sin2x7sinx+2=03\sin^{2}x - 7\sin x + 2 = 0in the interval [0,5π]\lbrack 0,5\pi\rbrack is

A

0

B

5

C

6

D

10

Answer

6

Explanation

Solution

3sin2x7sinx+2=03\sin^{2}x - 7\sin x + 2 = 03sin2x6sinxsinx+2=0(3sinx1)(sinx2)=03\sin^{2}x - 6\sin x - \sin x + 2 = 0 \Rightarrow (3\sin x - 1)(\sin x - 2) = 0,

But sinx2\sin x \neq 2 so sinx=13\sin x = \frac{1}{3}. Hence from 0to2π=20\text{to}2\pi = 2 solution's (one in Ist quadrant and other in 2nd quadrant), from 2πto 4π=22\pi\text{to }4\pi = 2 solution's and 4πto 5π=24\pi\text{to }5\pi = 2 solution's. So total number of solutions=6.= 6.