[tex] \frac{3}{x}
under the sign sin^{-1}
means the value of sin .
From right triangle we know that
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[tex]sin( \alpha )= \frac{opposite (leg)}{hypotenuse}
So, 3 is an opposite leg, and x is hypotenuse
cos( \alpha )= \frac{adjacent(leg)}{hypotenuse}
We know hypotenuse, we need to find the adjacent leg
(adj. leg)= \sqrt{ (hypotenuse)^{2}- (opposite /leg)^{2} }
(adj. leg)= \sqrt{ x^{2} - 3^{2} }
cos( \alpha ) = \frac{ \sqrt{ x^{2} -9} }{x}
This can be also written as
cos( \alpha ) = \frac{ ( x^{2} -9)^{ \frac{1}{2} } }{x}
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