Question

What is the value of PB if OP = 1 unit and $\angle POQ=\theta$?

• A. $sin\theta$
• B. $tan\theta$
• C. $sec\theta$
• D. $cot\theta$

Answer 1

The correct option is D

$cot\theta$

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,$\Delta PBO,cot\theta =\frac{PB}{PO}=\frac{PB}{1}=PB\Rightarrow PB=cot\theta$
$\therefore PB=cot\theta$