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sin 5 x-2sin 3x+ sin xProve that == tan xcossx-cos x |
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Answer» (sin5x-2sin3x+sinx)/(cos5x-cosx)=tanx LHS =[(sin5x-sin3x)-(sin3x-sinx)]/(cos5x-cosx) =[(2cos4x.sinx)-(2cos2x.sinx)]/(-2sin3x.sin2x) =2sinx.(cos4x-cos2x)/(-2sin3x.2sinx.cosx) =(cos4x-cos2x)/(-2sin3x.cosx) =(-2sin3x.sinx)/(-2sin3x,cosx) =(sinx)/(cosx) =tanx , Proved. |
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