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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

= tan (a)

We showed that the two sides could take the same form

\Rightarrow True

\frac{4 sec ( x ) - 4}{1 - cos ( θ )} = 4 sec (x)

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

sin (18 0^{\circ} + θ) = - sin (θ)

2 cos (x) \cdot csc^{2} (x) = 2 cot (x) \cdot csc (x)

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

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