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\( \theta_{1} \) and \( \theta_{2} \) are the inclination of lines \( L_{1} \) and \( L_{2} \), respectively, with \( x \)-axis. If \( L_{1} \) and \( L_{2} \) pass through \( P\left(x_{1}, y_{1}\right) \), then
\( \mathrm{P} \) equations of angle bisectors of lines are

W.
(1) \( \frac{x-x_{1}}{\cos \left(\frac{\theta_{1}+\theta_{2}}{2}\right)}=\frac{y-y_{1}}{\sin \left(\frac{\theta_{1}+\theta_{2}}{2}\right)} \)
(2) \( \frac{x-x_{1}}{-\sin \left(\frac{\theta_{1}-\theta_{2}}{2}\right)}=\frac{y-y_{1}}{\cos \left(\frac{\theta_{1}-\theta_{2}}{2}\right)} \)
(3) \( \frac{x-x_{1}}{\sin \left(\frac{\theta_{1}+\theta_{2}}{2}\right)}=\frac{y-y_{1}}{\cos \left(\frac{\theta_{1}+\theta_{2}}{2}\right)} \)
(4) \( \frac{x-x_{1}}{-\sin \left(\frac{\theta_{1}+\theta_{2}}{2}\right)}=\frac{y-y_{1}}{\cos \left(\frac{\theta_{1}+\theta_{2}}{2}\right)} \)
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