Asked by Natalie
Prove or disprove the following identity:
(sin(10x))/(sin(x)+sin(9x)) = (cos(5x))/(cos4x))
(sin(10x))/(sin(x)+sin(9x)) = (cos(5x))/(cos4x))
Answers
Answered by
Steve
sin(x)+sin(9x) = 2sin(5x)cos(4x), so
sin(10x)/(2sin(5x)cos(4x)) = cos(5x)/cos(4x)
sin(10x)cos(4x) = 2cos(5x)sin(5x)cos(4x)
sin(10x)cos(4x) = sin(10x)cos(4x)
QED
sin(10x)/(2sin(5x)cos(4x)) = cos(5x)/cos(4x)
sin(10x)cos(4x) = 2cos(5x)sin(5x)cos(4x)
sin(10x)cos(4x) = sin(10x)cos(4x)
QED
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