If 15 sin 4 α + 10 cos 4 α = 6 , for some α ∈ R , then the value of 27 sec 6 α + 8 cosec 6 α is equal to :

Step-by-step solution

15 sin 4 α + 10 cos 4 α = 6 15 sin 4 α + 10 cos 4 α = 6 sin 2 α + cos 2 α 2 3 sin 2 α - 2 cos 2 α 2 = 0 ∴   3 sin 2 α - 2 cos 2 α = 0 tan 2 α = 2 3   &   cot 2 α = 3 2 ⇒ 27 sec 6 α + 8 cosec 6 α = 27 sec 2 α 3 + 8 cosec 2 α 3 = 27 1 + tan 2 α 3 + 8 1 + cot 2 α 3 = 27 1 + 2 3 3 + 8 1 + 3 2 3 = 250