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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= - sin (x) + 1

Use the basic trigonometric identity:

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

= - \frac{1}{csc ( x )} + 1

= 1 - \frac{1}{csc ( x )}

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ( θ )}{1 - cos ( θ )} = csc (θ) + cot (θ)

cos^{2} (5 x) - sin^{2} (5 x) = cos (10 x)

cos (x) - sec (x) = - sin (x) tan (x)

tan (2 a) - tan (a) = tan (a) sec (2 a)

sin^{2} (x) - 4 cos^{2} (x) = 5 sin^{2} (x) - 4

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