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Bài 8 trang 161 SGK Đại số 10

Đề bài

Rút gọn các biểu thức sau:

a) 1+sin4acos4a1+cos4a+sin4a1+sin4acos4a1+cos4a+sin4a

b) 1+cosa1cosatan2a2cos2a1+cosa1cosatan2a2cos2a

c) cos2xsin4xcos6xcos2x+sin4xcos6xcos2xsin4xcos6xcos2x+sin4xcos6x

Hướng dẫn giải

a)1+sin4acos4a1+cos4a+sin4a=2sin22a+2sin2acos2a2cos22a+2sin2acos2a=2sin2a(sin2a+cos2a)2cos2a(sin2a+cos2a)=tan2a 

b)1+cosa1cosatan2a2cos2a=2cos2a22sin2a2.2sin2a22cos2a2cos2a2=1cos2a2=sin2a2 

c)cos2xsin4xcos6xcos2x+sin4xcos6x=(cos2xcos6x)sin4x(cos2xcos6x)+sin4x=2sin2x+6x2sin6x2x2sin4x2sin2x+6x2sin2x6x2+sin4x=2sin2x12sin2x+1