Question

化简:根号2sin(π/4-x)+根号6cos(π/4-x)

化简:根号2sin(π/4-x)+根号6cos(π/4-x)
(2)sin(67°-x)cos(x-22°)+cos(67°-x)cos(112°-x)的值为

Answer 1

V2sin(π/4-x)+V6cos(π/4-x)
=2V2[1/2sin(π/4-x)+V3/2 cos(π/4-x)]
=2V2 Sin(π/4-x+π/3)
=2V2 Sin(7π/12-x)

sin(67°-x)cos(x-22°)+cos(67°-x)cos(112°-x)
=sin(67°-x)cos(x-22°)+cos(67°-x)cos(90°-x+22°)
=sin(67°-x)cos(x-22°)+cos(67°-x)Sin(x-22°)
=sin(67°-x+x-22°)
=Sin(45°)
=V2/2