What is (cot(t))/(csc(t)-sin(t)) ?

The solution to (cot(t))/(csc(t)-sin(t)) is sec(t)

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simplify (cot(t))/(csc(t)-sin(t))

simplify

\frac{cot ( t )}{csc ( t ) - sin ( t )}

sec (t)

Solution steps

\frac{cot ( t )}{csc ( t ) - sin ( t )}

Simplify

csc (t) - sin (t) : cos (t) cot (t)

= \frac{cot ( t )}{cos ( t ) cot ( t )}

Cancel the common factor:

cot (t)

= \frac{1}{cos ( t )}

Use the basic trigonometric identity:

\frac{1}{cos ( x )} = sec (x)

= sec (t)

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What is (cot(t))/(csc(t)-sin(t)) ?
The solution to (cot(t))/(csc(t)-sin(t)) is sec(t)