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

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

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prove (cos(φ)+1)/(sin(φ)+tan(φ))=cot(φ)

prove

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

True

Solution steps

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

Manipulating left side

\frac{cos ( φ ) + 1}{sin ( φ ) + tan ( φ )}

Express with sin, cos

= \frac{cos ( φ )}{sin ( φ )}

Use the basic trigonometric identity:

\frac{cos ( x )}{sin ( x )} = cot (x)

= cot (φ)

We showed that the two sides could take the same form

\Rightarrow True

tan (x) + tan (x) = 0

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

- cot^{2} (x) = 1 - csc^{2} (x)

\frac{1}{tan ( 2 θ )} = \frac{cot ^{2} ( θ ) - 1}{2 cot ( θ )}

(1 - cos (θ)) + sin^{2} (θ) = 2

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