Question

find value of tan 13
$\pi$
divided by 12​

Answer 1

Answer:

2-√3

Step-by-step explanation:

tan(13π/12) = tan(π+π/12)

= tan(π/12) = tan(π/4-π/6)      

--------Using tan(x-y) = tanx-tany /(1+tan x tan y)------------

tan(π/4) - tan(π/6)/ (1+tan(π/4)tan(π/6)

= (1-1/√3)/(1+1/√3)

= (√3 - 1) / (√3+1)

= (√3 - 1)(√3 - 1) /(√3+1) (√3 - 1)

=(√3-1)² / (√3+1) (√3 - 1)

= (3+1-2√3) / (3-1)

=(4-2√3) / 2

=2-√3

Answer 2

Heya.......❤✌

Using tangent subtraction formula:

tan(A - B) = [tan(A) - tan(B)]/[1 + tan(A)tan(B)].

Hence,

tan(13π/12)

= tan(4π/3 - π/4)

= [tan(4π/3) - tan(π/4)]/[1 + tan(4π/3)tan(π/4)], from the above formula

= (-1 + √3)/(1 + √3)

= -(1 - √3)/(1 + √3)

= -(1 - √3)^2/[(1 + √3)(1 - √3)], (by rationalizing)

= -(1 - √3)^2/(1 - 3)

= (1/2)(1 - √3)^2

= (1/2)(1 - 2√3 + 3)

= (1/2)(4 - 2√3)

= 2 - √3.

Hope it’s helpful........ ☺