Prove that cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x).
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Step-by-step explanation:
LHS :
cot4x(sin5x+sin3x)
=cot4x×2sin(
2
5x+3x
)cos(
2
5x−3x
)
=
sin4x
cos4x
×2sin4xcosx=2cos4xcosx
RHS :
cotx(sin5x−sin3x)
=cotx×2sin(
2
5x−3x
)cos(
2
5x+3x
)
=
sinx
cosx
×2sinxcos4x=2cos4xcosx
Thus, LHS = RHS
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