How do you find all real numbers in the interval [0,360) that satisfy the equation and use degree measure $4sec^2(x)tan(x)=8tan(x)$ ?

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Answer 1 · 2015-12-06T10:53:35

$x=45^@$ , or $x=135^@$

Unless there are some typing mistake, you can simplify the tangent, as long as $x\ne 0$ :

$4sec^2(x)\cancel(tan(x))=8\cancel(tan(x))$

$4sec^2(x)=8$

$sec^2(x)=2$

And since $sec(x)=1/cos(x)$ , this means

$1/cos^2(x)=2 \implies cos^2(x)=1/2\implies cos(x)=\pm1/\sqrt(2)$

Which is true for $x=45^@$ , and $x=135^@$

How do you find all real numbers in the interval [0,360) that satisfy the equation and use degree measure 4sec^2(x)tan(x)=8tan(x)4sec^2(x)tan(x)=8tan(x)?