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

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

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

prove

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

True

Solution steps

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

Manipulating right side

csc (x) + cot (x)

Express with sin, cos

cot (x) + csc (x)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

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

Simplify

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

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

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

sin^{2} (θ) + cos^{2} (θ) = 1

sec (θ) - cos (θ) = sin (θ) tan (θ)

sin (x - \frac{π}{2}) = - cos (x)

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