Question

I need help answering this question for trig equations.
Sec^2x+4secx=-4

Answer 1

x = 120°

Explanation:

We are given;

sec²x + 4secx = -4

Rearranging gives;

sec²x + 4secx + 4 = 0

Factorizing the left hand side gives;

(sec x + 2)(sec x + 2) = 0

This means that;

(sec x + 2) = 0

From trigonometry, we know that sec x = 1/cos x

Thus;

(1/cos x) + 2 = 0

1/cos x = -2

cos x = -1/2

cos x = -0.5

x = cos^(-1) -0.5

x = 120°