Is (cos(u))/(1+tan(u))-(sin(u))/(1+cot(u))=cos(u)-sin(u) ?

The answer to whether (cos(u))/(1+tan(u))-(sin(u))/(1+cot(u))=cos(u)-sin(u) is True

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prove (cos(u))/(1+tan(u))-(sin(u))/(1+cot(u))=cos(u)-sin(u)

prove

\frac{cos ( u )}{1 + tan ( u )} - \frac{sin ( u )}{1 + cot ( u )} = cos (u) - sin (u)

True

Solution steps

\frac{cos ( u )}{1 + tan ( u )} - \frac{sin ( u )}{1 + cot ( u )} = cos (u) - sin (u)

Manipulating left side

\frac{cos ( u )}{1 + tan ( u )} - \frac{sin ( u )}{1 + cot ( u )}

Express with sin, cos

= cos (u) - sin (u)

We showed that the two sides could take the same form

\Rightarrow True

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

csc (θ) = \frac{1}{sec ( θ )}

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

\frac{csc ( z )}{sec ( z )} = cot (z)

\frac{tan ( θ ) cot ( θ )}{sec ( θ )} = cos (θ)

Is (cos(u))/(1+tan(u))-(sin(u))/(1+cot(u))=cos(u)-sin(u) ?
The answer to whether (cos(u))/(1+tan(u))-(sin(u))/(1+cot(u))=cos(u)-sin(u) is True