Question

Question #7f57e

Answer 1

Prove cos A = cos (-A)

Explanation:

We can prove it in 2ways:
a. By calculator.
Example cos 40 deg = 0.766 ; cos (-40) = 0.766.
Therefor: cos A = cos (-A)
b. By the trig unit circle.
On the trig unit circle, the axis OAx defines the trig function cos x.
The 2 arcs (AM = x) and (AM'= - x) have a common projection (On) on the cos axis.
Therefor cos x = cos (-x)
The angle <AOM is the angle x. On the trig unit circle, with radius = 1, the trig functions of the arc AM = x are the same trig functions of the angle <AOM = x.

Answer 2

Using Euler's formula ( `e^(alpha j) = cosalpha + j sinalpha` ) it can be proved that:

`cos(a-b) = cos a cos b + sin a sin b`

Taking a = 0 gives:

`cos(0-b) = cos 0 cos b + sin 0 sin b`
`cos(-b) = cos(b)`