prove sin(-x)=-sin(x)

Solution

prove

sin (- x) = - sin (x)

True

Solution steps

sin (- x) = - sin (x)

Manipulating left side

sin (- x)

Use the negative angle identity:

sin (- x) = - sin (x)

= - sin (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (x + π) = - sin (x)

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

(cot^{2} (x) + 1) (sin^{2} (x) - 1) = - cot^{2} (x)

\frac{cos ( 2 X )}{sin ( X )} + \frac{sin ( 2 X )}{cos ( X )} = csc (X)

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