Question

化简:根号2sin(π/4-x)+根号6cos(π/4-x)

（1）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

（1）化简:根号2sin(π/4-x)+根号6cos(π/4-x)
=2(根号2)[(1/2)sin(π/4-x)+(根号3)/2 *cos(π/4-x)]
=2(根号2)[sin(π/4-x)cos(π/3)+cos(π/4-x)sin(π/3)]
=2(根号2)sin[(π/4-x)+π/3]
=2(根号2)sin(7π/12 -x)

（2）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°)]
=sin45°
=(根号2)/2