t a n 6 2 0 o - 33 t a n 4 2 0 o + 27 t a n 2 2 0 o + 4 =

Step-by-step solution

Let, tan 20 o = k then, tan ⁡ 60 o = 3 tan ⁡ 20 o - t a n 3 2 0 o 1 - 3 t a n 2 20 o 3 = 3 k - k 3 1 - 3 k 2 3 1 - 3 k 2 2 = 3 k - k 3 2 3 1 + 9 k 4 - 6 k 2 = 9 k 2 + k 6 - 6 k 4 3 + 27 k 4 - 18 k 2 = 9 k 2 + k 6 - 6 k 4 k 6 - 33 k 4 + 27 k 2 - 3 = 0 k 6 - 33 k 4 + 27 k 2 + 4 = 7 Hence, t a n 6 2 0 o - 33 t a n 4 2 0 o + 27 t a n 2 2 0 o + 4 = 7