Question

The value of $\frac{\cos {12}^o-\sin {12}^o}{\cos {12}^o+\sin {12}^o}+\frac{\sin {147}^o}{\cos {147}^o}$ is :

• A. $1$
• B. $-1$
• C. $0$
• D. None of these

Answer 1

The correct option is C $0$

$\frac{\cos {12}^{\circ }-\sin {12}^{\circ }}{\cos {12}^{\circ }+\sin {12}^{\circ }}+\frac{\sin {147}^{\circ }}{\cos {147}^{\circ }}$

$\Rightarrow \frac{\cos {12}^{\circ }-\cos {78}^{\circ }}{\cos {12}^{\circ }+\cos {78}^{\circ }}+\frac{\sin (180-33)}{\cos (180-33)}$

$\Rightarrow \frac{-2\sin \left(\frac{(18+12)}{2}\right)\sin \left(\frac{12-78}{2}\right)}{2\cos \left(\frac{12+18}{2}\right)\cos \left(\frac{78-12}{2}\right)}-\frac{\sin 33}{\cos 33}$

$\Rightarrow -\frac{\sin \left({45}^o\right)\sin (-33)}{\cos \left(45\right)\cos \left(33\right)}-\frac{\sin \left(33\right)}{\cos \left(33\right)}$

$\Rightarrow \frac{\sin \left(33\right)}{\cos \left(33\right)}-\frac{\sin 33}{\cos 33}$

$\Rightarrow 0$