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The nubmber of solutions of x in the int...

The nubmber of solutions of x in the interval `[0,5pi]` satisfying the equation `3sin^(2)x-7sinx+2=0` is

A

0

B

5

C

6

D

10

Text Solution

Verified by Experts

The correct Answer is:
C
Given ,`3sin^(2)x-7sinx+2=0`
`rArr3sin^(2)x-6sinx-sinx-+2=0`
`rArr3sinx(sinx-2)-1(sinx-2)=0`
`rArr(3sinx-1)(sinx-2)=0`
`rArrsinx=(1)/(3)or2rArrsinx=(1)/(3) " " [becausesinxne2]`
`rArrx=sin^(-1)((1)/(3))`
Let `"sin"^(-1)(1)/(3)=alpha,0ltalphalt(pi)/(2),alphain[-(pi)/(2),(pi)/(2)]`
Then `alpha,pi-alpha,2pi+alpha,3pi-alpha,4pi+alpha,5pi-alpha` are the solutions in `[0,5pi]`.
`therefore` Required number of solutions are 6.
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