How do you find the general solutions for sec^2x-secx-2=0sec2x−secx−2=0?

1 Answer
Nghi N.
Aug 27, 2015

Solve sec^2 x - sec x - 2 = 0sec2x−secx−2=0

Ans: pi, +- pi/3π,±π3

Explanation:

Call sec = t, we get a quadratic equation:

t^2 - t - 2 = 0.t2−t−2=0.
Since (a - b + c = 0), use the shortcut. The 2 real roots are: t = - 1 and
t = - c/a = 2.t=−ca=2.

a. t = sec x = 1/cos x = - 1t=secx=1cosx=−1 --> cos x = - 1 cosx=−1--> x = pix=π

b. t = sec x = 1/cos x = 2t=secx=1cosx=2 --> cos x = 1/2cosx=12 --> x = +- pi/3x=±π3

General solutions:
x = pi + 2kpi = (2k+ 1)pix=π+2kπ=(2k+1)π
x = +- pi/4 + 2kpix=±π4+2kπ

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