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

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

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

prove

1 + sin (x) cot (x) = 1 + cos (x)

True

Solution steps

1 + sin (x) cot (x) = 1 + cos (x)

Manipulating left side

1 + sin (x) cot (x)

Express with sin, cos

1 + cot (x) sin (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

sin (x)

= cos (x)

= 1 + cos (x)

= 1 + cos (x)

= 1 + cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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