Auxilary angles (1 Viewer)

=)(= · Feb 7, 2022

I get 313 degrres as a solution but for some reason i also get 90 degrees as a solution but that isnt in the answer

=)(= · Feb 7, 2022

notme123 said:
heres a solution
$2\sec{x}-2\tan{x}=5$
$\frac{2}{\cos{x}}-\frac{2\sin{x}}{\cos{x}}=5$
$2-2\sin{x}=5\cos{x}$
$2\sin{x}+5\cos{x}=2$
$\sqrt{5^2+2^2}\sin(x+\tan^{-1}{\frac{5}{2}})=2$
$\sin(x+\tan^{-1}{\frac{5}{2}})=\frac{2}{\sqrt{29}}$
$x+\tan^{-1}{\frac{5}{2}}=21.8, 159.2, 201.8...$
for 0<x<360
$x=90, 133.6$
but x=90 is only a solution of $2\sin{x}+5\cos{x}=2$
not $2\sec{x}-2\tan{x}=5$
this is cuz $\sec{90}$ is undefined.

ohh makes sense thanks a lot

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