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(sinx + sin2x +sin3x) / (cosx + cos2x + cos3x) = tan2x

2 answers

tanx
= (cosx+cos3x)-cos2x/(sinx+sin3x)-sin2x
= 2cos2xcosx-cos2x/2sin2xcosx-sin2x (applying CD formulaes of sin and cos)
= cos2x(2cosx-1)/sin2x(2cosx-1)
= cos2x/sin2x
= cot2x
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