Find the Value of Tan 15 degrees ?

Solution :

The value of tan 15 degrees is \(\sqrt{3} – 1\over \sqrt{3} + 1\).

Proof : 

We write tan 15 as tan (45 – 30).

Using the formula of tan (A – B),

tan 15 = tan (45 – 30) = \(tan 45 – tan 30\over 1 + tan 45 tan 30\)

\(\implies\) tan 15 = \(1 – {1\over \sqrt{3}}\over 1 + {1\over \sqrt{3}}\) = \(\sqrt{3} – 1\over \sqrt{3} + 1\)

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