Question

If cos A COS = \(\frac{4}{5}\) 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 Correct Option is C

We are given that \( \cos A = \frac{4}{5} \). To find \( \tan A \), we can use the following trigonometric identity: \[ \tan A = \frac{\sin A}{\cos A} \] First, we need to find \( \sin A \). Using the Pythagorean identity: \[ \sin^2 A + \cos^2 A = 1 \] Substitute \( \cos A = \frac{4}{5} \) into the equation: \[ \sin^2 A + \left(\frac{4}{5}\right)^2 = 1 \] \[ \sin^2 A + \frac{16}{25} = 1 \] \[ \sin^2 A = 1 - \frac{16}{25} = \frac{25}{25} - \frac{16}{25} = \frac{9}{25} \] \[ \sin A = \frac{3}{5} \] Now, we can calculate \( \tan A \): \[ \tan A = \frac{\sin A}{\cos A} = \frac{\frac{3}{5}}{\frac{4}{5}} = \frac{3}{4} \]

The correct option is (C): \(\frac{4}{3}\)