Is (sin(θ))/(tan(θ))=cos(θ) ?

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

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prove (sin(θ))/(tan(θ))=cos(θ)

prove

\frac{sin ( θ )}{tan ( θ )} = cos (θ)

True

Solution steps

\frac{sin ( θ )}{tan ( θ )} = cos (θ)

Manipulating left side

\frac{sin ( θ )}{tan ( θ )}

Express with sin, cos

\frac{sin ( θ )}{tan ( θ )}

Use the basic trigonometric identity:

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

= \frac{sin ( θ )}{\frac{s i n ( θ )}{c o s ( θ )}}

Simplify

\frac{sin ( θ )}{\frac{s i n ( θ )}{c o s ( θ )}} : cos (θ)

\frac{sin ( θ )}{\frac{s i n ( θ )}{c o s ( θ )}}

Apply the fraction rule:

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

= \frac{sin ( θ ) cos ( 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

tan (x) csc (x) cos (x) = 1

cos (x) (tan (x) + cot (x)) = csc (x)

\frac{1}{1 - sin ^{2} ( y )} = 1 + tan^{2} (y)

csc (x) - cos^{2} (x) csc (x) = sin (x)

\frac{sin ( 2 x )}{1 + cos ( 2 x )} = tan (x)

Is (sin(θ))/(tan(θ))=cos(θ) ?
The answer to whether (sin(θ))/(tan(θ))=cos(θ) is True