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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

= \frac{1}{sin ( x ) + 1}

= \frac{1}{1 + sin ( x )}

We showed that the two sides could take the same form

\Rightarrow True

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

cot (t) tan (t) = 1

1 + tan^{2} (t) = sec^{2} (t)

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

\frac{cos ( θ )}{sin ( θ )} = cot (θ)

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