已知sin(a+π/4)=1/3,a∈(π/2,π)则sin2a=
问题描述:
已知sin(a+π/4)=1/3,a∈(π/2,π)则sin2a=
答
由sin(a+π/4)=1/3,a∈(π/2,π)即在第二象限,sinacosπ/4+cosasinπ/4=1/3(√2/2)sina+(√2/2)cosa=1/3两边平方得:(1/2)sin²a+sinacosa+(1/2)cos²a=1/9,sinacosa=1/9-1/2(∵sin²a+cos...