Question

Show that sin (x+64) cos(x+379)+sin (x+19)cos (x+244) =1÷square root of 2

Answer 1

Transformation :
sin α · cos β = 1/2 ( sin ( α - β ) + sin ( α + β ))
...= 1/2 ( sin ( - 375 ) + sin ( 2 x + 443 ) ) + 1/2 ( sin (-225)+ sin ( 2 x + 263 ))=
= 1/2 ( 1/√2 + sin ( 2 x + 443 ) + 1/2 ( 1/√2 + sin ( 2 x + 263 ) =
= 1/2√2 + 1/2√2 + 1/2 ( sin ( 2 x + 443 ) + sin ( 2 x + 263 ) ) = 
= 1/√2 + 1/2 · ( 2 · sin (( 4 x + 706 ) / 2) + cos ( 180 / 2 ) = 
( since cos 180°/2 = cos 90° = 0 )
= 1/√2 + 0 = 1/√2  ( correct )