Rewrite sin( π/4 ) cos ( π/4 ) + cos ( π/4 ) sin( π/4 ) as a single trigonometric ratio, and then determine its exact value.

Answer 1

Sum identity of sine is:

sin (α + β) = sin α • cos β + cos α • sin β

∴sin π/4 • cos π/4 + cos π/4 • sin π/4 = sin (π/4 + π/4)

=sin (π/2)

=1