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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

cot^{2} (x) - cos^{2} (x) cot^{2} (x) = cos^{2} (x)

cot (\frac{1}{x}) = cos (\frac{1}{x}) arcsin (\frac{1}{x})

\frac{tan ( x )}{sin ( x )} - sec (x) = 0

\frac{sec ^{2} ( y )}{tan ( y )} = tan (y) + cot (y)

cos (2 0^{\circ}) = - sin^{2} (θ)

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