Question

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

Answer 1

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`