How do I find the value of tan pi/12?

We have to find the value of tan (pi/12)

Solution

We know that pi=180 degrees

pi/12=180/12- 15 degrees

Now tan (pi.12) = tan 15

Tan 15°= Tan(45 – 30)°

By the trigonometry formula, we know,

Tan (A – B) = (Tan A – Tan B) /(1 + Tan A Tan B)

Therefore, we can write,

tan(45 – 30)° = tan 45° – tan 30°/1+tan 45° tan 30°

Now putting the values of tan 45° and tan 30° from the table we get;

tan(45 – 30)° = (1 – 1/√3)/ (1 + 1.1/√3)

tan (15°) = √3 – 1/ √3 + 1

Hence, the value oftan (15°)is √3 – 1/√3 + 1.

We can further resolve the above-resulted expression by putting the value of √3, which is equal to 1.732.

∴ Tan (15°) = (1.732 – 1)/(1.732 + 1) = 0.2679

Or tan (15°)0.27

Answer

tan(pi/12)= 0.27

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