sin（a+π/4）sin(a-π/4)=1/3,则cos4a=？
1个回答
展开全部
sin(a+π/4)sin(a-π/4)
=(sinacosπ/4+cosasinπ/4)(sinacosπ/4cosasinπ/4)
=[√2/2(sina+cosa)][√2/2(sina-cosa)]
=1/2(sin²a-cos²a)
=1/3
sin²a-cos²a=2/3
cos2a=cos²a-sin²a=-2/3
cos4a=2cos²2a-1
=2×(-2/3)²-1
=-1/9
=(sinacosπ/4+cosasinπ/4)(sinacosπ/4cosasinπ/4)
=[√2/2(sina+cosa)][√2/2(sina-cosa)]
=1/2(sin²a-cos²a)
=1/3
sin²a-cos²a=2/3
cos2a=cos²a-sin²a=-2/3
cos4a=2cos²2a-1
=2×(-2/3)²-1
=-1/9
本回答由提问者推荐
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
