The number of values of     in for which Option 1) 6 Option 2) 4 Option 3) 3 Option 4) 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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