Question

How do you simplify `cos(x - pi/2)`?

Answer 1

sinx

Explanation:

We can use `color(blue)"Addition formula"` to simplify

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

`rArrcos(x-pi/2)=cosxcos(pi/2)+sinxsin(pi/2)`

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

`rArrcos(x-pi/2)=cosx.0+sinx.1=sinx`