Is (sin(a))/(tan(a))=cos(a) ?

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

prove (sin(a))/(tan(a))=cos(a)

prove

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

True

Solution steps

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

Manipulating left side

\frac{sin ( a )}{tan ( a )}

Express with sin, cos

\frac{sin ( a )}{tan ( a )}

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Cancel the common factor:

sin (a)

= cos (a)

= cos (a)

= cos (a)

We showed that the two sides could take the same form

\Rightarrow True

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p ro v e \frac{csc ( θ ) + 1}{1 + sin ( θ )} = csc (θ)

p ro v e sec (A) csc (A) = csc (A) tan (A)

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