# If \sin(3x+5)=\cos(2x-10) what is the value of x?

If $\mathrm{sin}\left(3x+5\right)=\mathrm{cos}\left(2x-10\right)$ what is the value of x?
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casincal
This question is related to comparison of trigonometry function.
$\mathrm{sin}\left(3x+5\right)=\mathrm{cos}\left(2x-10\right)$
we know that
$\mathrm{sin}\left(90-A\right)=\mathrm{cos}A$
so,
$\mathrm{sin}\left(3x+5\right)=\mathrm{sin}\left(90-\left(2x-10\right)\right)$
Cancel sin from both side
$\mathrm{sin}\left(3x+5\right)=90-2x+10$
$3x+2x=100-5$
$5x=95$
$x=\frac{95}{5}=19$
$x=19$
Jeffrey Jordon