Example 17 Prove that
sin 5x-2sin 3x+ sin x
= tan x
C055I-C05 X
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Step-by-step explanation:
sin5x -2sin3x + sinx
sin5x - sin3x - sin3x + sinx
2cos(5x+3x)/2sin(5x-3x)/2 -( sin3x - sinx)
2cos4xsinx - 2cos2xsinx
2sinx(cos4x - cos2x)
2sinx 2sin3x (-sinx)
-4 sin^2x sin3x
-4sin^2xsin3xcosx/cosx
-4tanxsinxsin3x cosx
-tanx 2*2sinxcosx sin3x
-tanx 2 sin2x sin3x
-tanx (cosx - cos5x)
= tanx (cos5x - cosx)
RHS
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