Prove :
sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x cos 4x
Answers
Answered by
0
sinx+sin3x+sin5x+sin7x
sinx+7x+sin3x+sin5x
[sin(A+B)]sinC+sinD=2sin
2
C+D
cos
2
C−D
Now,
2sin(
2
x+7x
)cos(
2
x−7x
)+2sin(
2
3x+5x
)cos(
2
3x−5x
)
2sin4xcos3x+2sin4xcosx
2sin4x(cos3x+cosx)
2sin4x[2cos
2
C+D
cos
2
C−D
]
2sin4x[2cos
2
3x+x
cos
2
3x−x
]
2sin4x×2cos2xcosx
4sin4xcos2xcosx.
Answered by
1
Answer:
=(sin7x+sinx) +sin4x =sin(4x+ 3x) +sin(4x-3x) +sin4x
= so by using: sin(A+B) + sin(A-B) =2sins. cosB
= 2sin4x.cos3x+sin4x
Step-by-step explanation:
hope its helpful
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