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Find the value of tan60tan151+tan60tan15\dfrac{\tan 60^\circ - \tan 15^\circ}{1 + \tan 60^\circ \tan 15^\circ}

A1

B12\frac{1}{\sqrt{2}}

C12\frac{1}{2}

D32\frac{\sqrt{3}}{2}

Answer:

A. 1

Read Explanation:

Solution:

Given:


tan60tan151+tan60tan15\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


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