solve trigonometry equation

Question

Solve the equation sec(x + 30°) = 2 where -180° < x <180°.

Answer 1

The trigonometric equation sec(x + 30°) = 2

sec (x + 30°) = sec 60°

The genaral solution of sec(θ) = sec(α) is θ = 360° ± α, where n is an integer.

x + 30 = 360° ± 60°

x = 360 - 30 ± 60°

x = 330 ± 60°

The solutions are x = 390° and 270°.