Question

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(Cos a - cos 2a - cos 4a + cos 5a)/sina - sin 2a - sin 4a + sin 5a

Answer 1

$frac{(Cos alpha +Cos5 alpha) -(Cos2 alpha +Cos4 alpha )}{(Sin alpha +Sin5 alpha )-(Sin2 alpha +Sin4 alpha )} = frac{2Cos frac{ alpha +5 alpha }{2}Cos frac{ alpha -5 alpha }{2} -2Cos frac{2 alpha +4 alpha }{2} Cos frac{2 alpha -4 alpha }{2} }{2Sin frac{ alpha +5 alpha }{2}Cos frac{ alpha -5 alpha }{2}-2Sin frac{2 alpha +4 alpha }{2}Cos frac{2 alpha -4 alpha }{2} } =$$frac{2Cos3 alpha Cos2 alpha -2Cos3 alpha Cos alpha }{2Sin3 alpha Cos2 alpha -2Sin3 alpha Cos alpha }= frac{Cos3 alpha (Cos2 alpha -Cos alpha )}{Sin3 alpha (Cos2 alpha -Cos alpha )} = frac{Cos3 alpha }{Sin3 alpha } =Ctg3 alpha$

Answer 2

Спасибо)