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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating left 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{cos ( x )}{1 - sin ( x )} = tan (\frac{x}{2} - \frac{π}{4})

(sin (x))^{2} = sin^{2} (x)

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

cot (x - y) = \frac{cot ( x ) cot ( y ) + 1}{cot ( y ) - cot ( x )}

\frac{cot ( a )}{cos ( a )} = csc (a)

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