Question

Fine the value of.......
tan 15°​

Answer 1

Answer:

tan 30° = 1/√3

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 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

Explanation:

Before we try to find the tan 15 degrees value, let’s have a look at trigonometry table for sin, cos and tan.

Angle 0° 30° 45° 60° 90°

Sin θ 0 1/2 1/√2 √3/2 1

Cos θ 1 √3/2 1/√2 1/2 0

Tan θ 0 1/√3 1 √3 ∞

From the above table, we have the values of tan, sin and cos ratios for 0°, 30°, 45°, 60° and 90°. Now, by using these values, we have to find the value of tan (15°). Let’s get started,

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 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