化简:sin^2(A-30)+sin^2(A+30)-sin^2A
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/05 12:12:51
化简:sin^2(A-30)+sin^2(A+30)-sin^2A
化简:sin^2(A-30)+sin^2(A+30)-sin^2A
化简:sin^2(A-30)+sin^2(A+30)-sin^2A
sin^2(A-30)+sin^2(A+30)-sin^2A
=[1-cos(2A-60)]/2+[1-cos(2A+60)]/2+(cos2A-1)/2
=1/2-(cos2Acos60+sin2Asin60)-(cos2Acos60-sin2Asin60)+cos2A
=1/2-2cos2Acos60+cos2A
=1/2
sin^2(A-30)+sin^2(A+30)-sin^2A
=(sin(A-30)+sin(A+30))^2-2sin(A-30)sin(A+30)-4sin^2Acos^2A
=(1/2)sin^2A+(3/2)cos^2A-4sin^2Acos^2A
=4sin^4A-5sin^2A+(3/2)
我有八年没有做过了,可能做错了,呵呵,别见怪哈。
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