Use inverse functions

Question

2sin^2 x+11 cos x=7

Answer 1

2sin² x+11 cos x = 7

 

-2(1-cos² x) - 11 cos x + 7 = 0

 

2 cos² x - 11 cos x + 5 = 0

 

(2 cos x - 1)(cos x - 5) = 0

 

cos x = 1/2 (The alternative, cos x = 5 has no solution since cos x has range -1 ≤ cos x ≤ 1).

 

x = 2kπ ± π/3 ; k ∈ Z