Is (sin(t))/(1-cos(t))=csc(t)+cot(t) ?

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

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prove (sin(t))/(1-cos(t))=csc(t)+cot(t)

prove

\frac{sin ( t )}{1 - cos ( t )} = csc (t) + cot (t)

True

Solution steps

\frac{sin ( t )}{1 - cos ( t )} = csc (t) + cot (t)

Manipulating left side

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

Rewrite using trig identities

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

Manipulating right side

csc (t) + cot (t)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

coth^{2} (x) - csch^{2} (x) = 1

sin^{2} (2 x) + cos^{2} (2 x) = 1

\frac{( csc ^{2} ( x ) )}{cot ( x )} = csc (x) sec (x)

csc^{2} (x) (tan^{2} (x)) - 1 = tan^{2} (x)

sin (x) cos (x) + sin (3 x) sec (x) = tan (x)

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