Is (csc(a))/(csc(a)-sin(a))=sec^2(a) ?

The answer to whether (csc(a))/(csc(a)-sin(a))=sec^2(a) is True

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prove (csc(a))/(csc(a)-sin(a))=sec^2(a)

prove

\frac{csc ( a )}{csc ( a ) - sin ( a )} = sec^{2} (a)

True

Solution steps

\frac{csc ( a )}{csc ( a ) - sin ( a )} = sec^{2} (a)

Manipulating left side

\frac{csc ( a )}{csc ( a ) - sin ( a )}

Express with sin, cos

= \frac{1}{1 - sin ^{2} ( a )}

Manipulating right side

sec^{2} (a)

Express with sin, cos

= \frac{1}{cos ^{2} ( a )}

Rewrite using trig identities

= \frac{1}{1 - sin ^{2} ( a )}

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{( sin ^{2} ( θ ) )}{1 - cos ( θ )} = 1 + cos (θ)

\frac{( csc ( x ) )}{( cot ( x ) )} = sec (x)

9 sec^{2} (0) tan (0) = 12 tan (0)

cot (x) - sec (x) csc (x) cos (2 x) = tan (x)

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