Question

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

[1 Mark]
[Trigonometric Ratios]
[NCERT Exemplar]

$\frac{3}{5}$

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

Answer 1

The correct option is D $\frac{3}{4}$

The answer is (B).

According to the question, \( \cos A=4 / 5 \ldots(1) \) We know, \( \tan A =\sin A / \cos A \) To find the value of \( \sin A \), We have the equation, \( \sin ^{2} \theta+\cos ^{2} \theta=1 \) So, \( \sin \theta=\sqrt{ }\left(1-\cos ^{2} \theta\right) \) Then, \( \begin{array}{l} \sin A=\sqrt{ }\left(1-\cos ^{2} A\right) \\ \sin ^{2} A=1-\cos ^{2} A \\ \sin A=\sqrt{ }\left(1-\cos ^{2} A\right) \end{array} \) Substituting equation (1) in (2), We get, \( \begin{aligned} \operatorname{Sin} A & =\sqrt{ }\left(1-(4 / 5)^{2}\right) \\ & =\sqrt{ }(1-(16 / 25)) \\ & =\sqrt{ }(9 / 25) \\ & =3 / 4 \end{aligned} \) Therefore, \( \tan A=\frac{3}{5} \times \frac{5}{4}=\frac{3}{4} \)