Question

sinx + sin2x + sin3x + sin4x/cosx + cos2x + cos3x + cos4x

Answer 1

$\frac{sinx+sin2x+sin3x+sin4x}{cosx+cos2x+cos3x+cos4x} =\frac{(sinx+sin4x)+(sin2x+sin3x)}{(cosx+cos4x)+(cos2x+cos3x)} = \\ = \frac{2sin 2,5xcos1,5x+2sin2,5xcos0,5x}{2cos2,5xcos1,5x+2cos2,5xcos0,5x}= \frac{2sin2,5x(cos1,5x+cos0,5x)}{2cos2,5x(cos1,5x+cos0,5x)}= tg2,5x$