Is sin(θ)*cot(θ)=cos(θ) ?

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

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prove sin(θ)*cot(θ)=cos(θ)

prove

sin (θ) \cdot cot (θ) = cos (θ)

True

Solution steps

sin (θ) cot (θ) = cos (θ)

Manipulating left side

sin (θ) cot (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

\frac{1 + sec ( a )}{tan ( a ) + sin ( a )} = csc (a)

sin (4 x) = - 2 sin (2 x)

\frac{sin ( a )}{1 - cos ( a )} - cot (a) = csc (a)

2 sin^{2} (a) + cos^{2} (a) = 1 + sin^{2} (a)

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