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

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

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

prove

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

True

Solution steps

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

Manipulating right side

sin (x) cot (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

cos^{2} (\frac{θ}{2}) = \frac{sec ( θ ) + 1}{2 sec ( θ )}

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

2 cos^{2} (θ) tan (θ) = sin (2 θ)

sin^{5} (x) = (1 - cos^{2} (x))^{2} sin (x)

csc (x) sec (x) = cot (x) + tan (x)