Is csc(ω)-sin(ω)=cot(ω)cos(ω) ?

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

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prove csc(ω)-sin(ω)=cot(ω)cos(ω)

prove

csc (ω) - sin (ω) = cot (ω) cos (ω)

True

Solution steps

csc (ω) - sin (ω) = cot (ω) cos (ω)

Manipulating left side

csc (ω) - sin (ω)

Express with sin, cos

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

Rewrite using trig identities

= \frac{cos ^{2} ( ω )}{sin ( ω )}

Rewrite using trig identities

cos (ω) cot (ω)

= cot (ω) cos (ω)

We showed that the two sides could take the same form

\Rightarrow True

\frac{cot ( 3 θ ) - tan ( 3 θ )}{sin ( 3 θ ) + cos ( 3 θ )} = csc (3 θ) - sec (3 θ)

sin (- \frac{π}{2} - θ) = - cos (θ)

- 2 cos (2 x) \cdot sin (2 x) = sin (- 4 x)

sec^{2} (x) + tan (x) - 1 = 0

tan (a) cot (a) = 1

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