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) \cdot 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

2 sin^{2} (θ) + sin (θ) - 1 = 0

\frac{1}{csc ( t ) - cot ( t )} = csc (t) + cot (t)

sin (\frac{5 π}{2} + x) = cos (x)

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

cos (x) = sin (x + \frac{π}{6}) - sin (x - \frac{π}{6})