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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{csc ( t ) + 1}{cot ( t )}

Express with sin, cos

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

Rewrite using trig identities

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

Manipulating right side

\frac{cot ( t )}{csc ( t ) - 1}

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

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

tan (2 x) - tan (x) = tan (x) sec (2 x)

tan (x) sin (x) = sec (x) - cos (x)

(cos (x))^{2} = cos^{2} (x)

cos (2 a) = 2 cos^{2} (a) - 1

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