Is 1-(cos^2(a))/(1+sin(a))=sin(a) ?

The answer to whether 1-(cos^2(a))/(1+sin(a))=sin(a) is True

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prove 1-(cos^2(a))/(1+sin(a))=sin(a)

prove

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

True

Solution steps

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

Manipulating left side

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

Simplify

1 - \frac{cos ^{2} ( a )}{1 + sin ( a )} : \frac{1 + sin ( a ) - cos ^{2} ( a )}{1 + sin ( a )}

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

Rewrite using trig identities

= sin (a)

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ( x ) csc ( x )}{sec ( x )} = 1

\frac{sin ( 3 x ) - sin ( 5 x )}{2 cos ( 4 x )} = - sin (x)

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

tan (a) + cot (a) = 2 csc (2 a)

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

Is 1-(cos^2(a))/(1+sin(a))=sin(a) ?
The answer to whether 1-(cos^2(a))/(1+sin(a))=sin(a) is True