Question

Question 1
If $cosA=\frac{4}{5}$, then the value of tan A is

(A) $\frac{3}{5}$
(B) $\frac{3}{4}$
(C) $\frac{4}{3}$
(D) $\frac{5}{3}$

Answer 1

The answer is (B).

i) Firstly, we use the formula $sin\theta =\sqrt{1-co{s}^2\theta }$ to get the value of $sin\theta$

ii) Second, we use the formula $tan\theta =\frac{sin\theta }{cos\theta }$ to get the value of $tan\theta$

Given, $cosA=\frac{4}{5}$

$\therefore sinA=\sqrt{1-co{s}^{2}A}$

$\left[\begin{array}{c}\because si{n}^{2}A+co{s}^{2}S=2\\ \therefore sinA=\sqrt{1-co{s}^{2}A}\end{array}\right]$

$\sqrt{1-{\left(\frac{4}{5}\right)}^2}=\sqrt{1-\frac{16}{25}}=\sqrt{\frac{9}{25}}=\frac{3}{5}$

Now, $tanA=\frac{sinA}{cosA}=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4}$

Hence, the required value of tan A is $\frac{3}{4}$