Is (cot(y))/(sec(y))=csc(y)-sin(y) ?

The answer to whether (cot(y))/(sec(y))=csc(y)-sin(y) is True

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prove (cot(y))/(sec(y))=csc(y)-sin(y)

prove

\frac{cot ( y )}{sec ( y )} = csc (y) - sin (y)

True

Solution steps

\frac{cot ( y )}{sec ( y )} = csc (y) - sin (y)

Manipulating left side

\frac{cot ( y )}{sec ( y )}

Express with sin, cos

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

Manipulating right side

csc (y) - sin (y)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{cot ( x )} = tan (x)

csc (θ) = cos (θ) cot (θ) + sin (θ)

cos^{4} (x) + sin^{2} (x) cos^{2} (x) = cos^{2} (x)

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

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

Is (cot(y))/(sec(y))=csc(y)-sin(y) ?
The answer to whether (cot(y))/(sec(y))=csc(y)-sin(y) is True