Question

How do you prove `cos (theta + 2pi) = cos theta`?

Answer 1

see explanation

Explanation:

Using the appropriate `color(blue)" Addition formula "`

`color(red)(|bar(ul(color(white)(a/a)color(black)(cos(A±B)=cosAcosB∓sinAsinB)color(white)(a/a)|)))`

`rArrcos(theta+2pi)=costhetacos(2pi)-sinthetasin(2pi)`

now : `cos(2pi)=1" and " sin(2pi)=0`

`rArrcos(theta+2pi)=costheta .1-sintheta .0=costheta`