The number of values of   \alpha  in \left [ 0,2\pi \right ]for which 2\sin ^{3}\alpha -7\sin ^{2}\alpha +7\sin \alpha =2,\: \; is:

  • Option 1)

    6

  • Option 2)

    4

  • Option 3)

    3

  • Option 4)

    1

 

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^{3}\alpha -7\sin ^{2}\alpha +7sin\alpha =2

\Rightarrow (2sin^{2}\alpha -5sin\alpha +2) \: (sin\alpha -1)=0

\Rightarrow sin\alpha =1\ \, or\ \, sin\alpha =\frac{5\pm \sqrt{25-16}}{4}=\frac{8}{4}

Hence, possible solutions are sin\alpha=1 \: or \: \frac{1}{2}

Hence solutions are \frac{\pi }{6} \:, \frac{\pi }{2} \: and \: \frac{3\pi }{6}


Option 1)

6

This option is incorrect

Option 2)

4

This option is incorrect

Option 3)

3

This option is correct

Option 4)

1

This option is incorrect

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