sin(theta)*sin(3 theta)*sin(5 theta)
Answers
Answer:
sinθ+sin3θ+sin5θ=0
(sinθ+sin5θ)+sin3θ=0
2sin3xcos(−2x)+sin3x=0
2sin3x⋅cos2x+sin3x=0
⇒sin3x(2cos2x+1)=0
sin3x=0 2cos2x+1=0
3x=nπ cos2x=
2
−1
x=
3
nπ
,n∈z 2x=2π/3
General solution x=π/3
sin3x=0 x=
3
nπ
x=nπ±
3
π
.
cos2x=−
2
1
x=nπ±
3
π
n∈z.
Step-by-step explanation:
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Answer:
theta=nπ/3 or theta= nπ + or - π/3
Step-by-step explanation:
sin (theta+sin 5theta)+sin 3theta=0
2sin( theta+5theta/2) cos(theta-5theta/2)+sin 3theta=0
2sin 3theta cos 2theta +sin 3theta=0
sin 3theta(2cos2theta+1)=0
sin 3theta=0 or 2cos 2theta+1=0
theta=nπ/3 or theta= nπ +or- π/3