Question

If $\tan \theta =\frac{1}{\sqrt{5}}$ and $\theta$ lies in the first quadrant then the value of $\cos \theta$ is

• A. $\frac{1}{\sqrt{6}}$
• B. $-\frac{1}{\sqrt{6}}$
• C. $-\sqrt{\frac{5}{6}}$
• D. $\sqrt{\frac{5}{6}}$

Answer 1

Answer: (D)

$\sqrt{\frac{5}{6}}$

We know, $\tan \theta =\frac{\text{perpendicular}}{\text{base}}=\frac{1}{\sqrt{5}}$
Therefore, $\text{perpendicular}=1$ ...(i)
$\text{base}=\sqrt{5}$ ...(ii)
Hence, hypotenuse is
$=\sqrt{5+1}=\sqrt{6}$ ...(iii) .....(From (i) and (ii))
Therefore, $\cos \theta =\frac{\text{base}}{\text{hypotenuse}}$
$=\sqrt{\frac{5}{6}}$ .....From (ii) and (iii)
Hence answer is D