How do you find the general solutions for $sec^4x-4sec^2x=0$ ?

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Answer 1 · 2015-08-14T23:57:32

Solve sec^4 x - 4sec^2 x = 0

Ans: $+- pi/4$ and $+- (3pi)/4$

$1/cos^4 x - 4/cos^2 x = (1 - 4cos^2 x)/cos^4 x$ =

(1 - 2cos x)(1 + 2cos x) = 0

$a. 2cos x = 1$ --> $cos x = 1/2$ --> $x = +- pi/4$

$b. 1 + 2cos x = 0$ --> $cos = -1/2$ --> $x = +- (3pi)/4$

How do you find the general solutions for sec^4x-4sec^2x=0sec^4x-4sec^2x=0?