Question

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

Answer 1

Формулы:

$sinalpha -sinbeta =2sinfrac{alpha-beta}{2}cosfrac{alpha+beta}{2}\ \cosalpha +cosbeta =2cosfrac{alpha+beta}{2}cosfrac{alpha-beta}{2}\ \ \ \ frac{sin6alpha -sin2alpha}{cos6alpha+cos2alpha} =frac{2sinfrac{6alpha-2alpha}{2}cosfrac{6alpha+2alpha}{2}}{2cosfrac{6alpha+2alpha}{2}cosfrac{6alpha-2alpha}{2}} =frac{2sin2alphacdot cos4alpha}{2cos4alphacdot cos2alpha} =tg2alpha$