Question

Write the solution set of the equation (2 cos x + 1) (4 cos x + 5) = 0 in the interval (0, 2 π].

Answer 1

8 cos²x +10 cos x + 4 cos x + 5 = 0 

8 cos²x +14 cos x + 5 = 0 

Solving the quadratic equation, we get, 

cos x = - 0.5 

cos x = cos 120° 

x = 2nπ ± \(\frac{2π}3\)

So x = \(\frac{2π}3\)where n = 0,

And when n =1 x = \(\frac{4π}3\)