Question

What is the value of tan 15 =

Answer 1

❥${\red{\underline{\underline{\bold{Answer:-}}}}}$

Value of tan15° is √3 -1/√3 +1 or 0.27(≈).

❥${\red{\underline{\underline{\bold{Explanation:-}}}}}$

Tan 15° = Tan(45 – 30)°

By the trigonometry formula, we know,

Tan (A – B) = (TanA – TanB) /(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 of tan (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 2

$\bf{\underline{\underline{Answer:}}}$

tan (15°) = 2 - √3

$\bold \green{\underline {Step\:by\:step\:explanation:-}}$

Tan (30° ) = tan (2*15°)

1/√3 = 2 tan (15°) / (1- tan ²(15°))

√3 = (1- tan ²(15°) / 2 tan (15°)

tan ²(15°) + 2√3 tan (15°) -1 =0

tan (15°) = -2√3 + √ (2√3)² -4 (1)(-1) / 2(1)

= -2√3±√16 / 2

= -√3±2

So,

tan (15°) = 2 - √3 or - (2 + √3)

As, tan 15° falls in the first quadrant, tan (15°) > 0

Therefore,

tan (15°) = 2 - √3

On simplification we get, 0.26794919243.