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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating right side

csc (x) - sin (x)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

1 - 4 sin^{2} (x) cos^{2} (x) = cos^{2} (2 x)

sin (3 x) = sin (x) (4 cos^{2} (x) - 1)

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

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

cos (x) - csc (x) cot (x) = - cos (x) cot^{2} (x)

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