(a) tan 55°

$\frac{\cos 10^{\circ}+\sin 10^{\circ}}{\cos 10^{\circ}-\sin 10^{\circ}}$

$=\frac{1+\tan 10^{\circ}}{1-\tan 10^{\circ}} \quad\left[\right.$ Dividing the numerator and denominator by $\left.\cos 10^{\circ}\right]$

$=\frac{\tan 45^{\circ}+\tan 10^{\circ}}{1-\tan 45^{\circ} \times \tan 10^{\circ}}$

$=\tan \left(45^{\circ}+10^{\circ}\right) \quad\left[\quad U \operatorname{sing} \tan (A+B)=\frac{\tan A+\tan B}{1-\tan A \tan B}\right]$

$=\tan 55^{\circ}$