Question

\( \tan 15^\circ + \tan 75^\circ = \)

• A. \( \sqrt{5} + 1 \)
• B. \(2 \)
• C. \( \sqrt{7} - 1 \)
• D. \(4 \)
• E. \(0 \)

Hint:

Use complementary angle identities: \( \tan(90^\circ-\theta)=\cot\theta \).

Answer 1

The Correct Option is D

Concept: \[ \tan(90^\circ - \theta) = \cot \theta \]

Step 1: Use identity.
\[ \tan 75^\circ = \cot 15^\circ = \frac{1}{\tan 15^\circ} \]

Step 2: Use known value.
\[ \tan 15^\circ = 2 - \sqrt{3} \] \[ \tan 75^\circ = 2 + \sqrt{3} \]

Step 3: Add.
\[ (2 - \sqrt{3}) + (2 + \sqrt{3}) = 4 \]