Question

Write `cos{(pi-:4)-a}` in terms of trigonometric ratios of just `a`?

Answer 1

`cos{(pi-:4)-a}=1/sqrt2(cosa+sina)`

Explanation:

As `Cos(A-B)=cosAcosB+sinAsinB`

`cos{(pi-:4)-a}=cos(pi/4-a)`

= `cos(pi/4)cosa+sin(pi/4)sina`

= `1/sqrt2cosa+1/sqrt2sina`

= `1/sqrt2(cosa+sina)`