Question

Value of tan15degree ?

Answer 1

tan(15) = sin(15) / cos(15) = sin(45 - 30) / cos(45 - 30) = [ sin(45)cos(30) - sin(30)cos(45) ] / [ cos(45)cos(30) + sin(45)sin(30)] Since sin(45) = cos(45) = √2/2, you can just factor that out from the top and bottom [ cos(30) - sin(30) ] / [ cos(30) + sin(30)] [ √3/2 - 1/2 ] / [ √3/2 + 1/2] (√3 - 1) / (√3 + 1) (√3 - 1)^2 / (√3+1)(√3 - 1) (√3 - 1)^2 / (3 - 1) (3 - 2√3 +1) / 2 =2 - √3

Answer 2

Let us use the Half Angle formula to solve this.

tan (∅/2) = sin∅/(1+cos∅)

In this question, the angle given is 15° = (30/2)°

Inputting this in the Half Angle Formula, we get:
tan(30/2) = sin(30/2) ÷ {1 + cos(30/2)}  ---------------- (i)

We know Sin30 = 1/2 and Cos30=(√3)/2. Inputting these values in (i), we get the value of tan (30/2) = 1/2 ÷ {1 + (√3/2)} = 1 / (2 + √3)

Value of Tan15 = 0.268