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

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

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

prove

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

True

Solution steps

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

Manipulating left side

1 + cot (x)

Express with sin, cos

1 + cot (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

Multiply:

1 \cdot sin (x) = sin (x)

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

cos (3 b) = cos (b) (cos^{2} (b) - 3 sin^{2} (b))

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

sec (b) - (tan (b)) (sin (b)) = cos (b)

tan (θ) = 2 sin (θ)

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

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