Question

Find the value of $\dfrac{\tan 60^\circ - \tan 15^\circ}{1 + \tan 60^\circ \tan 15^\circ}$

• A. 1
• B. $$\frac{1}{\sqrt{2}}$$
• C. $$\frac{1}{2}$$
• D. $$\frac{\sqrt{3}}{2}$$

Answer 1

Answer:

A. 1

Solution:

Given:

$\dfrac{\tan 60^\circ - \tan 15^\circ}{1 + \tan 60^\circ \tan 15^\circ}$

Formula:

tan (A - B) = (tan A - tan B)/(1 + tan A tan B)

tan 45° = 1

Calculation:

(tan 60° - tan 15°)/(1 + tan 60° tan 15°)

⇒ tan (60° - 15°)

⇒ tan 45°

⇒ 1