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

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

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

prove

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

True

Solution steps

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

Manipulating left 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

p ro v e sin (π + x) = - sin (x)

p ro v e 1 + tan^{2} (α) = \frac{1}{cos ^{2} ( α )}

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

p ro v e \frac{sec ^{2} ( θ )}{sec ^{2} ( θ ) - 1} = csc^{2} (θ)

p ro v e cos (π - θ) = - cos (θ)