Is (sec(x))/(-csc(x))+(-sin(x))/(cos(x))=-2tan(x) ?

The answer to whether (sec(x))/(-csc(x))+(-sin(x))/(cos(x))=-2tan(x) is True

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prove (sec(x))/(-csc(x))+(-sin(x))/(cos(x))=-2tan(x)

prove

\frac{sec ( x )}{- csc ( x )} + \frac{- sin ( x )}{cos ( x )} = - 2 tan (x)

True

Solution steps

\frac{sec ( x )}{- csc ( x )} + \frac{- sin ( x )}{cos ( x )} = - 2 tan (x)

Manipulating left side

\frac{sec ( x )}{- csc ( x )} + \frac{- sin ( x )}{cos ( x )}

Express with sin, cos

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

Rewrite using trig identities

- 2 tan (x)

We showed that the two sides could take the same form

\Rightarrow True

1 = \frac{sec ( u ) + tan ( u )}{sec ( u ) + tan ( u )}

\frac{sin ^{2} ( x )}{1} \cdot \frac{1}{sin ^{2} ( x )} = 1

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

cos^{2} (2 x) - sin^{2} (2 x) = 0

cos (x + \frac{π}{6}) = \frac{3}{2} cos (x) - \frac{1}{2} sin (x)

Is (sec(x))/(-csc(x))+(-sin(x))/(cos(x))=-2tan(x) ?
The answer to whether (sec(x))/(-csc(x))+(-sin(x))/(cos(x))=-2tan(x) is True