Is (sec(t)-cos(t))/(sec(t))=sin^2(t) ?

The answer to whether (sec(t)-cos(t))/(sec(t))=sin^2(t) is True

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prove (sec(t)-cos(t))/(sec(t))=sin^2(t)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= 1 - cos^{2} (t)

Rewrite using trig identities

= sin^{2} (t)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{tan ( x )} + tan (x) = sec (x) csc (x)

sin (\frac{π}{2} - x) = sin (\frac{π}{2} + x)

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

tan (θ) + cot (θ) = 2 csc (2 θ)

csc^{4} (x) - cot^{4} (x) = 2 cot^{2} (x) + 1

Is (sec(t)-cos(t))/(sec(t))=sin^2(t) ?
The answer to whether (sec(t)-cos(t))/(sec(t))=sin^2(t) is True