Question

If $\sin \theta +cosec\theta =2$, then the value of ${\sin }^9\theta +cose{c}^9\theta$ is

• A. 3
• B. 2
• C. 4
• D. 1

Answer 1

The correct option is B 2

Consider the given equation.

$\sin \theta +cosec\theta =2$

$\sin \theta +\frac{1}{\sin \theta }=2$

${\sin }^2\theta +1=2\sin \theta$

${\sin }^2\theta -2\sin \theta +1=0$

${(\sin \theta -1)}^2=0$

$\sin \theta =1$

Therefore,

$cosec\theta =\frac{1}{\sin \theta }=1$

Now,

${\sin }^9\theta +{cosec}^9\theta ={\left(1\right)}^9+{\left(1\right)}^9=2$

Hence, B will be correct answer.