Is cot(θ)sin(θ)=cos(θ) ?

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

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prove cot(θ)sin(θ)=cos(θ)

prove

cot (θ) sin (θ) = cos (θ)

True

Solution steps

cot (θ) sin (θ) = cos (θ)

Manipulating left side

cot (θ) sin (θ)

Express with sin, cos

cot (θ) sin (θ)

Use the basic trigonometric identity:

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

= \frac{cos ( θ )}{sin ( θ )} sin (θ)

Simplify

\frac{cos ( θ )}{sin ( θ )} sin (θ) : cos (θ)

\frac{cos ( θ )}{sin ( θ )} sin (θ)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

sin (θ)

= cos (θ)

= cos (θ)

= cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

cot (x) (sec^{2} (x) - 1) = tan (x)

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

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

sin (θ) (tan (θ) + cot (θ)) = sec (θ)

cot (2 θ) = \frac{cot ^{2} ( θ ) - 1}{2 cot ( θ )}