急cos(6θ)cos(2θ)sin(4θ)sin(6θ)sin(8θ)cos(θ)cos(5θ)+cos(7θ)sin(3θ)−sin(4θ)cos(4θ)−cos(5θ)sin(9θ)−sin(−θ)sin(θ)+cos(θ)cos(θ)−sin(θ)

Question

急
cos(6θ)cos(2θ)
sin(4θ) sin(6θ)
sin(8θ) cos(θ)
cos(5θ) + cos(7θ)
sin(3θ) − sin(4θ)
cos(4θ) − cos(5θ)
sin(9θ) − sin(−θ)
sin(θ)
+ cos(θ)
cos(θ)
− sin(θ)

Answer 1

cos(6θ)cos(2θ)=1/2[cos8θ+cos4θ]
sin(4θ) sin(6θ)=-1/2[cos10θ-cos2θ]
sin(8θ) cos(θ)=1/2[sin9θ+sin7θ]
cos(5θ) + cos(7θ)=2cos6θcosθ
sin(3θ) − sin(4θ)=-2cos(7θ/2)sin(θ/2)
cos(4θ) − cos(5θ)=2sin(9θ/2)sin(θ/2)
sin(9θ) − sin(−θ)=2sin5θcos4θ
sin(θ) + cos(θ)=√2sin(θ+π/4)
cos(θ) − sin(θ)==√2cos(θ+π/4)