prove cos(x)=cos(-x)

Solution

prove

cos (x) = cos (- x)

True

Solution steps

cos (x) = cos (- x)

Manipulating left side

cos (x)

Use the negative angle identity:

cos (- x) = cos (x)

= cos (- x)

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) = \frac{1}{csc ( θ )}

tan (θ) = \frac{sin ( θ )}{cos ( θ )}

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

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

\frac{1}{cot ( x ) + 1} + \frac{1}{tan ( x ) + 1} = 1