Задание:
Докажите тождество: cos2x cos12x+sin2x sin12x=cos10x
Решение:
cos2xcos (10x+2x)+sin2xsin (10x+2x)=cos2x (cos10xcos2x-sin10xsin2x)+sin2x (sin10xcos2x+sin2xcos10x)=cos^2xcos10x-sin10xsin2xcos2x+sin10xcos2xsin2x=sin^2xcos10x=cos^2xcos10x+sin^2xcos10x=cos10x (cos^2x+sin^2x)=cos10x*1=cos10X
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