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

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

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

prove

cot (x) sin (x) = cos (x)

True

Solution steps

cot (x) sin (x) = cos (x)

Manipulating left side

cot (x) sin (x)

Express with sin, cos

cot (x) sin (x)

Use the basic trigonometric identity:

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

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

Simplify

\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)

= cos (x)

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e sin (2 x) + cos (2 x) - 1 = 2 sin (x) (cos (x) - sin (x))

p ro v e (csc^{2} (x) - 1) sin (x) = cot (x) cos (x)

p ro v e cot (x) (1 - cos^{2} (x)) = \frac{1}{2} sin (2 x)

p ro v e \frac{sec ^{2} ( t )}{tan ( t )} = sec (t) csc (t)

p ro v e cos (x) (tan^{2} (x) + 1) = sec (x)