Evaluate tan 15°

To find : tan 15° degree value

Tan 15° = tan (45° – 30°)

We know that the formula,

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

Now substitute the value of tan 30° and tan 45°

\(\tan 15^{\circ}=\tan (45^{\circ}-30^{\circ})=(\tan 45^{\circ}-\tan 30^{\circ})/(1+\tan 45^{\circ}\tan 30^{\circ})\)

\(\tan 15^{\circ}=(1-\frac{1}{\sqrt{3}})/(1+\frac{1}{\sqrt{3}})\)

Therefore, \(\tan 15^{\circ}=(\sqrt{3}-1)/(\sqrt{3}+1)\)

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