Is (sec(x)csc(x))/(csc^2(x))=tan(x) ?

The answer to whether (sec(x)csc(x))/(csc^2(x))=tan(x) is True

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prove (sec(x)csc(x))/(csc^2(x))=tan(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{1 - sin ( x )} - \frac{1}{1 + sin ( x )} = \frac{2 tan ( x )}{cos ( x )}

cot (b) sin (b) = cos (b)

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

csc (2 x) = \frac{1 + cot ^{2} ( x )}{2 cot ( x )}

(1 - cos (θ)) (1 + cos (θ)) (1 + cot^{2} (θ)) = 1

Is (sec(x)csc(x))/(csc^2(x))=tan(x) ?
The answer to whether (sec(x)csc(x))/(csc^2(x))=tan(x) is True