Question

How do you simplify `cos ( pi - a ) + sin ( (pi/2) + a)`?

Answer 1

0

Explanation:

Using the following `color(blue)"Addition formulae"`

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

`color(red)(|bar(ul(color(white)(a/a)color(black)(sin(A±B)=sinAcosB±cosAsinB)color(white)(a/a)|)))`

`rArrcos(pi-a)+sin(pi/2+a)`
`"------------------------------------------------"`

`cos(pi-a)=cos(pi)cosa+sin(pi)sina=-cosa`

`sin((pi/2)+a)=sin(pi/2)cosa+cos(pi/2)sina=cosa`
`"---------------------------------------------------"`

adding these 2 results together.

`rArrcos(pi-a)+sin((pi/2)+a)=-cosa+cosa=0`