The equality cos 4x(sin 5x+sin 3x)=cot x(sin 5x-sin 3x) holds for some real value of x
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ANSWER
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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