Bài 8 trang 161 SGK Đại số 10
Đề bài
Rút gọn các biểu thức sau:
a) 1+sin4a−cos4a1+cos4a+sin4a1+sin4a−cos4a1+cos4a+sin4a
b) 1+cosa1−cosatan2a2−cos2a1+cosa1−cosatan2a2−cos2a
c) cos2x−sin4x−cos6xcos2x+sin4x−cos6xcos2x−sin4x−cos6xcos2x+sin4x−cos6x
Hướng dẫn giải
a)1+sin4a−cos4a1+cos4a+sin4a=2sin22a+2sin2acos2a2cos22a+2sin2acos2a=2sin2a(sin2a+cos2a)2cos2a(sin2a+cos2a)=tan2a
b)1+cosa1−cosatan2a2−cos2a=2cos2a22sin2a2.2sin2a22cos2a2−cos2a2=1−cos2a2=sin2a2
c)cos2x−sin4x−cos6xcos2x+sin4x−cos6x=(cos2x−cos6x)−sin4x(cos2x−cos6x)+sin4x=−2sin2x+6x2sin6x−2x2−sin4x−2sin2x+6x2sin2x−6x2+sin4x=2sin2x−12sin2x+1