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How do you simplify ${(tan (x))}^{2} sin (x) csc (x)$ $(tan(x))^2 sin(x) csc(x)$ ?

1 Answer

Jul 24, 2015

${(tan (x))}^{2} sin (x) csc (x) = {(tan (x))}^{2}$ $(tan(x))^2sin(x)csc(x) = (tan(x))^2$
$XXXX$ $color(white)("XXXX")$ provided $x \neq n π$ $x != npi$ for any $n epsilon ZZ$
$color(white)("XXXX")$ otherwise the left side is undefined

Explanation:

This follows from the definition:
$color(white)("XXXX")$ $csc(x) = 1/sin(x)$
So
$color(white)("XXXX")$ $sin(x)csc(x) = 1$

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