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Question
Options
tan 55°
cot 55°
−tan 35°
−cot 35°
Solution
\[\frac{\cos10^\circ + \sin10^\circ}{\cos10^\circ - \sin10^\circ}\]
\[ = \frac{1 + \tan10^\circ}{1 - \tan10^\circ} \left[\text{ Dividing the numerator and denominator by }\cos 10^\circ \right]\]
\[ = \frac{\tan45^\circ + \tan10^\circ}{1 - \tan45^\circ \times \tan10^\circ}\]
\[ = \tan(45^\circ + 10^\circ) \left[\text{ Using }\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \right]\]
\[ = \tan55^\circ\]
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