Question

The value of $\frac{\cos 12^{\circ}-\sin 12^{\circ}}{\cos 12^{\circ}+\sin 12^{\circ}}+\frac{\sin 147^{\circ}}{\cos 147^{\circ}}$ is equal to

(A) 1

(B) -1

(C) 0

(D) None of these

Answer 1

$\text { } \begin{array}{l} \frac{\cos 12^{\circ}-\sin 12^{\circ}}{\cos 12^{\circ}+\sin 12^{\circ}}+\frac{\sin 147^{\circ}}{\cos 147^{\circ}} \\=\frac{1-\tan 12^{\circ}}{1+\tan 12^{\circ}}+\tan 147^{\circ} \\=\tan \left(45^{\circ}-12^{\circ}\right)+\tan \left(180^{\circ}-33^{\circ}\right) \\=\tan 33^{\circ}-\tan 33^{\circ}=0\end{array}$

So, The correct option will be (C).