Question

$\frac{\cos 10°+\sin 10°}{\cos 10°-\sin 10°}=$

(a) tan 55°
(b) cot 55°
(c) −tan 35°
(d) −cot 35°

Answer 1

(a) $\tan 55°$

$$\begin{gathered} \frac{\cos 10°+\sin 10°}{\cos 10°-\sin 10°} \\ =\frac{1+\tan 10°}{1-\tan 10°}\left[\mathrm{Dividing}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}\cos 10°\right] \\ =\frac{\tan 45°+\tan 10°}{1-\tan 45°\times \tan 10°} \\ =\tan (45°+10°)\left[\mathrm{Using}\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}\right] \\ =\tan 55° \end{gathered}$$