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

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

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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

tan (2 x) = \frac{2 tan ( x )}{1 - tan ^{2} ( x )}

(tan (θ) + cot (θ)) sin (θ) = sec (θ)

sin (x) csc (x) = 1

sin (2 x) + cos (2 x) - 1 = 2 sin (x) (cos (x) - sin (x))

cos^{2} (θ) = 1 - sin^{2} (θ)