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

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

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

prove

sin (x) \cdot 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

(csc (θ) - cot (θ)) (csc (θ) + cot (θ)) = 1

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

csc (x) - sin (x) = (cot (x)) (cos (x))

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

sin^{2} (θ) cos (θ) sec (θ) = 1 - cos^{2} (θ)