Question

If sinA + cosA=√2sinA , then what is the value of tan A ?

• A. √2
• B. 1
• C. √2 + 1
• D. √2 - 1

Answer 1

Answer:

C. √2 + 1

Given:

$\sin A + \cos A = \sqrt{2}\sin A$

Rearrange:

$\cos A = (\sqrt{2}-1)\sin A$

Divide both sides by $(\cos A):$

$1 = (\sqrt{2}-1)\tan A$

Therefore,

$\tan A = \frac{1}{\sqrt{2}-1}$

Rationalize the denominator:

$\tan A$
$= \frac{1}{\sqrt{2}-1}\cdot\frac{\sqrt{2}+1}{\sqrt{2}+1}$
$= \frac{\sqrt{2}+1}{2-1}$
$\tan A = \sqrt{2}+1$