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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Use the negative angle identity:

sin (- x) = - sin (x)

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

Use the negative angle identity:

cos (- x) = cos (x)

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

Simplify

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

Use the basic trigonometric identity:

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

= tan (a)

We showed that the two sides could take the same form

\Rightarrow True

\frac{csc ( z )}{sec ( z )} = cot (z)

2 cos (x) sin (x) = sin (2 x)

\frac{( 1 - cos ( a ) )}{1 + cos ( a )} = tan^{2} (\frac{a}{2})

cos (x - y) = cos (y - x)

\frac{sec ^{2} ( x )}{csc ^{2} ( x )} = tan^{2} (x)

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