Question

Prove the following:

`cos(pi/4 + x) + cos(pi/4 - x) = sqrt(2)cosx`

Answer 1

L.H.S. = `cos(pi/4 + x) + cos(pi/4 - x)`

= `2cos([pi/4 + x + pi/4 - x)/2)cos((pi/4 + x - (pi/4 - x))/2)`

= `2cos  pi/4 cosx`

= `2(1/sqrt(2))cosx`

= `sqrt(2)cosx`

= R.H.S.