10^ + 10^ 10^ - 10^ is equal to: - Vidyadip

MCQ

$\frac{\cos10^\circ+\sin10^\circ}{\cos10^\circ-\sin10^\circ}$ is equal to:

✓
$\tan55^\circ$
B
$\cot55^\circ$
C
$-\tan35^\circ$
D
$-\cot35^\circ$

✓

Answer

Correct option: A.

$\tan55^\circ$

$\frac{\cos10^\circ+\sin10^\circ}{\cos10^\circ-\sin10^\circ}$
$=\frac{1+\tan10^\circ}{1-\tan10^\circ}$
$[$Dividing the numerator and denominator by $\cos10^\circ]$
$=\frac{\tan45^\circ+\tan10^\circ}{1-\tan45^\circ\times\tan10^\circ}$
$=\tan(45^\circ+10^\circ)$ $\Big[$Using $\tan(\text{A+B})=\frac{\tan\text{A}+\tan\text{B}}{1-\tan\text{A}\tan\text{B}}\Big]$
$=\tan55^\circ$

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