Question

In the given circle, OP = 1 unit and ∠POQ=θ
Which of the following is $cosec\theta$ from this circle?

• A. OB
• B. OA
• C. AP
• D. AB

Answer 1

The correct option is A

OB

As we can see from the above figure,
$\angle BOQ={90}^{\circ }$
So,$\angle BOP={90}^{\circ }-\angle POQ={90}^{\circ }-\theta$
In,$\Delta BPO,\angle BPO={90}^{\circ }$ $(\because PBistangenttothecircle)$
In,$\Delta BPO,\angle BOP+\angle PBO={90}^{\circ }\Rightarrow \angle PBO={90}^{\circ }-({90}^{\circ }-\theta )=\theta$
In,$\Delta PBO,cosec\theta =\frac{OB}{PO}=\frac{OB}{1}=OB$

So, $cosec\theta$ = OB