Is cot(t)cos(t)=csc(t)-sin(t) ?

The answer to whether cot(t)cos(t)=csc(t)-sin(t) is True

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prove cot(t)cos(t)=csc(t)-sin(t)

prove

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

True

Solution steps

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

Manipulating right side

csc (t) - sin (t)

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

cos (t) cot (t)

= cot (t) cos (t)

We showed that the two sides could take the same form

\Rightarrow True

sin (\frac{3 π}{2} - x) = - cos (x)

sin (x) sec (x) = \frac{1}{cot ( x )}

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

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

(1 - sin (x)) (1 + csc (x)) = csc (x) - sin (x)

Is cot(t)cos(t)=csc(t)-sin(t) ?
The answer to whether cot(t)cos(t)=csc(t)-sin(t) is True