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

  • Option 1)

    4

  • Option 2)

    6

  • Option 3)

    1

  • Option 4)

    2

 

Answers (1)

As we learnt in 

Trigonometric Equations -

The equations involving trigonometric function of unknown angles are known as trigonometric equations.

- wherein

e.g. \cos ^{2}\Theta - 4\cos \Theta = 1

 

 2\sin ^2 x + 5\sin x-3=0   \Rightarrow \sin x= \frac{-5 \pm \sqrt{25+24}}{4}

\Rightarrow \sin x= \frac{-5 \pm 7}{4}   \Rightarrow \sin x = \frac{1}{2}                      \left[sin\ x \neq -3]

Now, in rage \left [ 0,3\pi \right ]

\sin x=\frac{1}{2}   is satisfied by 

x = \frac{\pi }{6}, \frac{5\pi }{6}, \frac{13\pi }{6},\frac{17\pi }{6}

4 solution


Option 1)

4

Correct

Option 2)

6

Incorrect

Option 3)

1

Incorrect

Option 4)

2

Incorrect

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