Is (sec(t))/(cos(t))-(tan(t))/(cot(t))=1 ?

The answer to whether (sec(t))/(cos(t))-(tan(t))/(cot(t))=1 is True

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prove (sec(t))/(cos(t))-(tan(t))/(cot(t))=1

prove

\frac{sec ( t )}{cos ( t )} - \frac{tan ( t )}{cot ( t )} = 1

True

Solution steps

\frac{sec ( t )}{cos ( t )} - \frac{tan ( t )}{cot ( t )} = 1

Manipulating left side

\frac{sec ( t )}{cos ( t )} - \frac{tan ( t )}{cot ( t )}

Express with sin, cos

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

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

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

\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

Is (sec(t))/(cos(t))-(tan(t))/(cot(t))=1 ?
The answer to whether (sec(t))/(cos(t))-(tan(t))/(cot(t))=1 is True