simplify (cos3x +i sin3x)^5 (cosx-i sinx)^3/(cos5x + i sin5x)^7 (cos2x - i sin2x)^5
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Answered by
1
Answer:
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Answered by
0
Answer:
We have,
L.H.S.
cosx−cos3x−cos5x+cos7x
sinx−sin3x+sin5x−sin7x
=
(cosx−cos5x)−(cos3x−cos7x)
(sinx+sin5x)−(sin3x+sin7x)
=
2sin(
2
x+5x
)sin(
2
5x−x
)−2sin(
2
3x+7x
)sin(
2
7x−3x
)
2sin(
2
x+5x
)cos(
2
x−5x
)−2sin(
2
3x+7x
)cos(
2
3x−7x
)
=
sin3xsin2x−sin5xsin2x
sin3xcos(−2x)−sin5xcos(−2x)
=
sin3xsin2x−sin5xsin2x
cos2xsin3x−sin5xcos2x
=
sin2x(sin3x−sin5x)
cos2x(sin3x−sin3x)
=cot2x
L.H.S.=R.H.S.
Step-by-step explanation:
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