Question

The solution($\theta$) for ${\text{cosec}}^2\theta -2\text{cosec}\theta +1=0,0⩽\theta ⩽\frac{\pi }{2},$ is

• A. ${90}^0$
• B. ${45}^0$
• C. ${30}^0$
• D. none of these

Answer 1

The correct option is A ${90}^0$

${\text{cosec}}^2\theta -2\text{cosec}\theta +1=0\Rightarrow \frac{1}{{\sin }^2\theta }-2\frac{1}{\sin \theta }+1=0$

Multiplying both sides by $\sin \theta$

$\Rightarrow {\sin }^2\theta -2\sin \theta +1=0\Rightarrow (sin\theta -1{)}^2=0\Rightarrow \sin \theta =1\Rightarrow \theta ={90}^0$ $as(0\le \theta \le \frac{\pi }{2})$

Therefore, Answer is ${90}^0$