Question

Find \( \tan 15^\circ + \tan 45^\circ \).

• A. \( 1 + \tan 15^\circ \)
• B. \( \tan 60^\circ \)
• C. \( \tan 60^\circ + 1 \)
• D. \( \tan 15^\circ + 1 \)

Hint:

Use known trigonometric values such as \( \tan 45^\circ = 1 \) to simplify calculations. For non-standard angles like \( 15^\circ \), use a calculator or approximation techniques.

Answer 1

The Correct Option is B

\( \tan 15^\circ + \tan 45^\circ \).

1. Step 1: Use the known value of \( \tan 45^\circ \): We know that \( \tan 45^\circ = 1 \).

2. Step 2: Add the values of \( \tan 15^\circ \) and \( \tan 45^\circ \): Thus, the expression becomes: \[ \tan 15^\circ + \tan 45^\circ = \tan 15^\circ + 1 \] Using a calculator or a known trigonometric value for \( \tan 15^\circ \), we find: \[ \tan 15^\circ \approx 0.2679 \] So, \[ \tan 15^\circ + \tan 45^\circ = 0.2679 + 1 \approx
1.2679 \] Thus, the correct answer is \( \tan 60^\circ \) which is approximately \(
1.2679 \), corresponding to option (B).