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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

= tan (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (β) - sin^{2} (β) = 2 cos^{2} (β) - 1

(1 - cos (β)) (1 + cos (β)) = \frac{1}{csc ^{2} ( β )}

\frac{cot ( θ ) sec ( θ )}{csc ( θ )} = 1

sin (θ) csc (θ) - cos^{2} (θ) = sin^{2} (θ)

tan^{2} (θ) + 1 = \frac{1}{cos ^{2} ( θ )}

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