若a为锐角,cos(a+30)=4/5,则sin(2a+15)=
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若a为锐角,cos(a+30)=4/5,则sin(2a+15)=
2012江苏高考数学第11题
2012江苏高考数学第11题
![若a为锐角,cos(a+30)=4/5,则sin(2a+15)=](/uploads/image/z/8195522-50-2.jpg?t=%E8%8B%A5a%E4%B8%BA%E9%94%90%E8%A7%92%2Ccos%28a%2B30%29%3D4%2F5%2C%E5%88%99sin%282a%2B15%29%3D)
a∈(0,90)
a+30∈(30,120)
sin(a+30)>0
sin(a+30)=3/5
sin(2a+60)=2sin(a+30)cos(a+30)=24/25
又cos(a+30)>cos45,a+30∈(30,120)
∴30
a+30∈(30,120)
sin(a+30)>0
sin(a+30)=3/5
sin(2a+60)=2sin(a+30)cos(a+30)=24/25
又cos(a+30)>cos45,a+30∈(30,120)
∴30
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