Question

If $\cos A=\frac{4}{5}$, then the value of $\tan A$ (in first quadrant) is:

• A. $\frac{3}{5}$
• B. $\frac{3}{4}$
• C. $\frac{4}{3}$
• D. $\frac{5}{3}$

Answer 1

Answer: (B)

$\frac{3}{4}$

Given that, $\cos A=\frac{4}{5}$

We know that $\sec A=\frac{1}{\cos A}$

$\therefore \sec A=\frac{5}{4}$

We also know that, $\tan A=\sqrt{{\sec }^{2}A-1}$

$\therefore \tan A=\sqrt{\frac{25}{16}-1}$

$=\frac{3}{4}$ (considering $A$ lies in the first quadrant)

Hence, $\tan A=\frac{3}{4}$