Is csc(x)-sin(x)=cot(x)*cos(x) ?

The answer to whether csc(x)-sin(x)=cot(x)*cos(x) is True

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prove csc(x)-sin(x)=cot(x)*cos(x)

prove

csc (x) - sin (x) = cot (x) \cdot cos (x)

True

Solution steps

csc (x) - sin (x) = cot (x) cos (x)

Manipulating left 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 )}

Rewrite using trig identities

cos (x) cot (x)

= cot (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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

1 - sin^{2} (- θ) = cos^{2} (θ)

tan (θ) csc^{2} (θ) - tan (θ) = cot (θ)

\frac{1 + sec ( θ )}{csc ( θ )} - tan (θ) = sin (θ)

\frac{1 + cot ( x )}{1 + tan ( x )} = cot (x)

Is csc(x)-sin(x)=cot(x)*cos(x) ?
The answer to whether csc(x)-sin(x)=cot(x)*cos(x) is True