My answer was tan 30 + tan 45
[ 3 + (square root of) 3 ] / 3.
is that right?
5 Answers

tan( 5π/12) =
tan(3π/12 + 2π/12) =
tan( π/4 + π/6) =
[ tan(π/4) + tan(π/6) ] / [ 1 – tan(π/4)•tan(π/6)] =
[ 1 + 1/√3 ] / [ 1 – 1 • 1/√3] =
[ (3 + √3) /3 ] / [ (3 – √3) / 3] =
(3 + √3) / (3 – √3) =
(3 + √3)² / (9 – 3) =
(9 + 6√3 + 3) / 6 =
(12 + 6√3) / 6 =
2 + √3
see the link for a table of trig identities, in particular tangent of a sum.

No you can’t just add.
Even though you can’t use calculator for finding solution, you should at least use calculator for verifying answer.
5π/12 = 75°
Actual value: tan (75°) = 3.732 (using calculator)
Your solution: (3+√3)/3 = 1.57735
So this is obviously not right
Use angle sum identity:
tan(75°) = tan(45°+30°)
tan(75°) = (tan(45°)+tan(30°)) / (1 – tan(45°)*tan(30°))
tan(75°) = (1 + √3/3) / (1 – 1*√3/3)
tan(75°) = ((3+√3)/3) / ((3√3)/3)
tan(75°) = (3+√3) / (3√3)
tan(75°) = (3+√3)(3+√3) / (3√3)(3+√3)
tan(75°) = (9+6√3+3) / (93)
tan(75°) = (12+6√3) / 6
tan(75°) = 2 + √3
Check using calculator
tan(75°) = 3.7320508075688772935274463415059
2 + √3 = 3.7320508075688772935274463415059
ok

30 + tan 45
[ 3 + (square root of) 3 ] / 3.
was the answer i got as well i am sure it is right

no
ans = tan (30 +45) does not = tan 30 + tan 45
need formula that reduces tan(a+b) to simpler form
in terms of sin/ cos a and b

Find Exact Value Of Tan