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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{sec ^{2} ( a ) cot ( a )}{csc ^{2} ( a )}

Express with sin, cos

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

Use the basic trigonometric identity:

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

= tan (a)

We showed that the two sides could take the same form

\Rightarrow True

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

sec (x) = sin (x) (cot (x) + tan (x))

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

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

\frac{tan ^{2} ( θ ) + 1}{tan ^{2} ( θ )} = csc^{2} (θ)

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