Is cot(t)csc(t)=(csc^2(t)-1)/(cos(t)) ?

The answer to whether cot(t)csc(t)=(csc^2(t)-1)/(cos(t)) is True

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prove cot(t)csc(t)=(csc^2(t)-1)/(cos(t))

prove

cot (t) csc (t) = \frac{csc ^{2} ( t ) - 1}{cos ( t )}

True

Solution steps

cot (t) csc (t) = \frac{csc ^{2} ( t ) - 1}{cos ( t )}

Manipulating left side

cot (t) csc (t)

Express with sin, cos

= \frac{cos ( t )}{sin ^{2} ( t )}

Manipulating right side

\frac{csc ^{2} ( t ) - 1}{cos ( t )}

Express with sin, cos

= \frac{1 - sin ^{2} ( t )}{cos ( t ) sin ^{2} ( t )}

Rewrite using trig identities

= \frac{cos ( t )}{sin ^{2} ( t )}

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{1 + sin ( t )} = (sec (t) - tan (t)) sec (t)

\frac{1 - cos ( x )}{1 + cos ( x )} = tan^{2} (\frac{x}{2})

sin (\frac{π}{3}) = \frac{3}{2}

\frac{tan ( x )}{1 - cos ( x )} = csc (1 + sec (x))

cos (t) sec (\frac{π}{2} - t) = cot (t)

Is cot(t)csc(t)=(csc^2(t)-1)/(cos(t)) ?
The answer to whether cot(t)csc(t)=(csc^2(t)-1)/(cos(t)) is True