Question

find the value od Tan15°​

Answer 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.

Answer 2

Answer:

tan 15° = √3 – 1/ √3 + 1

Step-by-step explanation:

Similarly, we can also find the value of tangent 15 degrees, by knowing the value of sin 15 and cos 15 degrees.

Tan (15°) = sin 15/cos 15

Tan 15° = sin 15/cos 15

Sin 15° = sin (45 – 30)° and cos 15 = cos (45 – 30)°

∴ tan (15°) =  sin (45 – 30)° /cos (45 – 30)°

From the trigonometry formulas, we know,

sin(A – B) = sin A cos B – cos A sin B

and cos (A – B) = cos A cos B + sin A sin B

Therefore,

tan (15°)= (sin 45° cos 30° – cos 45° sin 30°)/ (cos 45° cos 30° + sin 45° sin 30°)

Putting the values of sin 30°, sin 45°, cos 30° and cos 45°, we get,

tan 15° = (1/√2.√3/2 – 1/√2.½) / (1/√2.√3/2 + 1/√2.½)

Solving the above equation we have,

tan 15° = √3 – 1/ √3 + 1