Question

Упростите с подробным решением
(sin6a-sin2a)/(cos6a+cos2a)

Answer 1

Формулы:

$sin\alpha -sin\beta =2sin\frac{\alpha-\beta}{2}cos\frac{\alpha+\beta}{2}\\ \\cos\alpha +cos\beta =2cos\frac{\alpha+\beta}{2}cos\frac{\alpha-\beta}{2}\\ \\ \\ \\ \frac{sin6\alpha -sin2\alpha}{cos6\alpha+cos2\alpha} =\frac{2sin\frac{6\alpha-2\alpha}{2}cos\frac{6\alpha+2\alpha}{2}}{2cos\frac{6\alpha+2\alpha}{2}cos\frac{6\alpha-2\alpha}{2}} =\frac{2sin2\alpha\cdot cos4\alpha}{2cos4\alpha\cdot cos2\alpha} =tg2\alpha$