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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{tan ( θ ) csc ( θ )} = cos (θ)

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

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

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

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

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