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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

= cot (x)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{tan ^{2} ( x ) + 1}{tan ^{2} ( x )} = csc^{2} (x)

sin (7 x) + sin (x) = 2 cos (3 x) sin (4 x)

\frac{csc ( 4 x ) - cot ( 4 x )}{csc ( 4 x ) + cot ( 4 x )} = tan (2 x)

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

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