Is 1/(cos(x))-cos(x)=sin(x)tan(x) ?

The answer to whether 1/(cos(x))-cos(x)=sin(x)tan(x) is True

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prove 1/(cos(x))-cos(x)=sin(x)tan(x)

prove

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

True

Solution steps

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

Manipulating right side

sin (x) tan (x)

Express with sin, cos

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

Rewrite using trig identities

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

Expand

\frac{1 - cos ^{2} ( x )}{cos ( x )} : \frac{1}{cos ( x )} - cos (x)

= - cos (x) + \frac{1}{cos ( x )}

= \frac{1}{cos ( x )} - cos (x)

We showed that the two sides could take the same form

\Rightarrow True

sec (u) cos (u) - sin^{2} (u) = cos^{2} (u)

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

tan^{2} (x) cot^{2} (x) = 1

cos (π + θ) = - cos (θ)

cos (\frac{3 π}{2} - θ) = - sin (θ)

Is 1/(cos(x))-cos(x)=sin(x)tan(x) ?
The answer to whether 1/(cos(x))-cos(x)=sin(x)tan(x) is True