Is (cos(a))/(tan(a))=csc(a)-sin(a) ?

The answer to whether (cos(a))/(tan(a))=csc(a)-sin(a) is True

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prove (cos(a))/(tan(a))=csc(a)-sin(a)

prove

\frac{cos ( a )}{tan ( a )} = csc (a) - sin (a)

True

Solution steps

\frac{cos ( a )}{tan ( a )} = csc (a) - sin (a)

Manipulating left side

\frac{cos ( a )}{tan ( a )}

Express with sin, cos

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

Manipulating right side

csc (a) - sin (a)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

sin (π + θ) = - sin (θ)

\frac{tan ( x ) cot ( x )}{sin ( x )} = csc (x)

csc^{2} (\frac{θ}{2}) = \frac{2 sec ( θ )}{sec ( θ ) - 1}

Is (cos(a))/(tan(a))=csc(a)-sin(a) ?
The answer to whether (cos(a))/(tan(a))=csc(a)-sin(a) is True