Question

If \( \sin x = \frac{3}{5} \), then the value of \( \sec x + \tan x \) is equal to:

• A. -2
• B. 3
• C. 0
• D. 2
• E. -3

Hint:

Use the identity \( \sin^2 x + \cos^2 x = 1 \) to find \( \cos x \), then use \( \sec x = \frac{1}{\cos x} \) and \( \tan x = \frac{\sin x}{\cos x} \) to calculate \( \sec x + \tan x \).

Answer 1

The Correct Option is D

Step 1: We are given that \( \sin x = \frac{3}{5} \). 
We can use the Pythagorean identity \( \sin^2 x + \cos^2 x = 1 \) to find \( \cos x \): \[ \cos^2 x = 1 - \sin^2 x = 1 - \left( \frac{3}{5} \right)^2 = 1 - \frac{9}{25} = \frac{16}{25} \] \[ \cos x = \frac{4}{5} \] Step 2: Now, we compute \( \sec x + \tan x \): \[ \sec x = \frac{1}{\cos x} = \frac{1}{\frac{4}{5}} = \frac{5}{4}, \quad \tan x = \frac{\sin x}{\cos x} = \frac{\frac{3}{5}}{\frac{4}{5}} = \frac{3}{4} \] \[ \sec x + \tan x = \frac{5}{4} + \frac{3}{4} = \frac{8}{4} = 2 \]