Toán Lớp 11: Rút gọn 2sin(2x+pi/3)+4cosxcos(x+pi/3)

Question

Toán Lớp 11:  Rút gọn 2sin(2x+pi/3)+4cosxcos(x+pi/3)

landinhngoc97 · Answer

$2 sin left(2x+ dfrac{ pi}{3} right)+2. Big(  cos left(2x+ dfrac{ pi}{3} right)+ cos dfrac{ pi}{3} Big)$   $=2 Big(  sin left(2x+ dfrac{ pi}{3} right)+ cos left(2x+ dfrac{ pi}{3} right)  Big)+2. cos dfrac{ pi}{3}$   $=2 Big(  sin left(2x+ dfrac{ pi}{3} right)+ cos left(2x+ dfrac{ pi}{3} right)+1$   $=2. sqrt2 sin left(2x+ dfrac{ pi}{3}+ dfrac{ pi}{4} right)+1$   $=2 sqrt2 sin left(2x+ dfrac{7 pi}{12} right)+1$

minhhaanh · Answer

Giải đáp:   $2 sqrt 2 sin left(2x+ dfrac{7 pi}{12} right)+1$    Lời giải và giải thích chi tiết:   $2 sin left(2x+ dfrac{ pi}{3} right)+4 cos x cos left(x+ dfrac{ pi}{3} right)$   $=2 sin left(2x+ dfrac{ pi}{3} right)+4. dfrac{1}{2} bigg[ cos left(2x+ dfrac{ pi}{3} right)+ cos left(- dfrac{ pi}{3} right) bigg]$   $=2 sin left(2x+ dfrac{ pi}{3} right)+2 cos left(2x+ dfrac{ pi}{3} right)+2 cos dfrac{ pi}{3}$   $=2 sqrt 2 sin left(2x+ dfrac{ pi}{3}+ dfrac{ pi}{4} right)+2. dfrac{1}{2}$   $=2 sqrt 2 sin left(2x+ dfrac{7 pi}{12} right)+1$.