Question

Как найти тангенс пи/12?

Answer 1

when x/2 = pi/12

x = 2(pi/12) = pi/6

so when tan(x/2) = sinx /(1 + cosx)

so tan(pi/12) = sin(pi/6) / [1 + cos(pi/6)]

now substitute sin(pi/6) = 1/2 and

cos(pi/6) = √3/2

tan(pi/12) = (1/2) / (1 + √3/2) = (1/) / (2 + √3)

now rationalize the denominator by multiplying with (2 - √3) / (2 -√3)

tan(pi/12) = (2 - √3) / (2 + √3)(2 - √3)

tan(pi/12) = (2 - √3) /(4 - 3) = (2 - √3)