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

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

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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{tan ^{2} ( θ )}{1 - cos ^{2} ( θ )} = sec^{2} (θ)

cos (o) = \frac{1}{sec ( o )}

sin (x) = \frac{sec ( x )}{tan ( x ) + cot ( x )}

(cot (x) + 1)^{2} = csc^{2} (x) + 2 cot (x)

sin (θ) = - cos (θ + \frac{π}{2})

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