Question

The set of solution(s) of 2 cos^2
(θ) - 13 cos(θ) + 6 = 0 that is(are) in the
interval (0,π/2) is one of following
a. {π/6} b. {π/3}
c. {π/4}
d. {π/3, π/6}
e. {π/6, π/4}

Answer 1

This is just a quadratic in cosθ

2cos^2θ - 13cosθ + 6 = 0
(2cosθ - 1)(cosθ - 6) = 0

so,
2cosθ = 1
cosθ = 1/2
θ = π/3

or,
cosθ = 6
no solutions there