How do you solve $2-10secx=4-9secx$ for $0<=x<=2pi$ ?

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Answer 1 · 2016-11-13T20:41:10

$x=(2pi)/3, x=(4pi)/3$

$2-10secx=4-9secx$

Isolate $secx$ :
$2-secx=4$
$-secx=2$

$secx=-2$

To solve for x, I find it easier when I'm working in terms of sin, cos, or tan rather than sec, so I'll convert it:

$1/cosx=-2$

$-2cosx=1$
$cosx=-1/2$

*Remember our domain is restricted to $0<=x<=2pi$
$x=(2pi)/3, x=(4pi)/3$

How do you solve 2-10secx=4-9secx2-10secx=4-9secx for 0<=x<=2pi0<=x<=2pi?