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

1 Answer

Aug 14, 2015

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

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

Explanation:

#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#

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