Задание:
Sin75+sin45/sin285 вычислите
Решение:
sin (75°)+sin (45°) /sin (285°)=sin (30°+45°)+sin (45°) / (sin (180°+(60°+45°)=sin (30°) cos (45°)+cos (30°) sin45°)+sin (45°) / (-sin (60°+45°)=(1/2)*(1/sqrt (2)+(sqrt (3)*(1/sqrt (2)+(1/sqrt (2) / (- (sin (60°) cos (45°)+cos (60°)*sin (45°)=(1+sqrt (3) /2sqrt (2)+(1/sqrt (2) / (- (sqrt (3) /2) (1/sqrt (2)+(1/2) (1/sqrt (2)=(1+sqrt (3) /2sqrt (2)+(1/sqrt (2) / (- (1/sqrt (2) (1+sqrt (3) /2)=(1/2sqrt (3) /2sqrt (3) -2sqrt (2) / (1+sqrt (3)=(sqrt (3) -2) / (sqrt (2)+sqrt (6)
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