If = a b then + - = - Vidyadip

MCQ

If $\tan\theta = \frac{\text{a}}{\text{b}}$ then $\frac{\cos\theta+\sin\theta}{\cos\theta-\sin\theta}=$

A
$\frac{\text{a}-\text{b}}{\text{a + b}}$
B
$\frac{\text{b}-\text{b}}{\text{b+a}}$
✓
$\frac{\text{b + a}}{\text{b}-\text{a}}$
D
None of these

✓

Answer

Correct option: C.

$\frac{\text{b + a}}{\text{b}-\text{a}}$

Given : $\tan\theta = \frac{\text{a}}{\text{b}}$
Dividing all terms of $\frac{\cos\theta+\sin\theta}{\cos\theta-\sin\theta}$ by $\cos\theta$
$=\frac{1+\tan\theta}{1-\tan\theta} =\frac{1+\frac{\text{a}}{\text{b}}}{1-\frac{\text{a}}{\text{b}}} = \frac{\text{b + a}}{\text{b}-\text{a}}$

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