prove tan(-x)=-tan(x)

Solution

prove

tan (- x) = - tan (x)

True

Solution steps

tan (- x) = - tan (x)

Manipulating left side

tan (- x)

Use the negative angle identity:

tan (- x) = - tan (x)

= - tan (x)

We showed that the two sides could take the same form

\Rightarrow True

csc^{2} (x) (1 - cos^{2} (x)) = 1

cot (θ) = \frac{sin ( 2 θ )}{1 - cos ( 2 θ )}

\frac{1 + sin ( θ )}{cos ( θ )} = sec (θ) + tan (θ)

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

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