How do you solve $sec^2(x) - sec(x) = 2$ ?

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Answer 1 · 2015-12-04T10:35:29

$x= \pi + 2k\pi$

$x = \pi/3 + 2k\pi$

$x= -pi\/3 + 2k\pi$

Since $sec(x)=1/cos(x)$ , the expression becomes

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

Assuming $cos(x)\ne 0$ , we can multiply everything by $cos^2(x)$ :

$1-cos(x) = 2cos^2(x)$ .

Rearrange:

$2cos^2(x)+cos(x)-1=0$ .

Set $t=cos(x)$ :

$2t^2+t-1=0$

Solve as usual with the discriminant formula:

$t=-1$ , $t=1/2$

Convert the solutions:

$cos(x)=-1 \iff x=\pi+2k\pi$

$cos(x)=1/2 \iff x=\pm\pi/3 +2k\pi$

How do you solve sec^2(x) - sec(x) = 2sec^2(x) - sec(x) = 2?