Is 1/(1-sin(x))=-csc(x) ?

The answer to whether 1/(1-sin(x))=-csc(x) is False

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prove 1/(1-sin(x))=-csc(x)

prove

\frac{1}{1 - sin ( x )} = - csc (x)

False

Solution steps

\frac{1}{1 - sin ( x )} = - csc (x)

Show that the two sides are not equal

For

\frac{1}{1 - sin ( x )} = - csc (x)

plug in

x = 1

\frac{1}{1 - sin ( 1 )} = 6.30799 \dots

\frac{1}{1 - sin ( 1 )}

Refine to a decimal form

= 6.30799 \dots

- csc (1) = - 1.18839 \dots

- csc (1)

Refine to a decimal form

= - 1.18839 \dots

The two sides are not equal

\Rightarrow False

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