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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

cos (x) = cos (- x)

sin (θ) = \frac{1}{csc ( θ )}

tan (θ) = \frac{sin ( θ )}{cos ( θ )}

(sin^{2} (x) - 1) (sec^{2} (x) - 1) = - sin^{2} (x)

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

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