已知cos(15°+a)=4/5,a为锐角,详细题目如下已知cos(15°+a)=4/5,a为锐角,求sin(435°-a)+sin(a-165°) /cos(195°+a)的值.请写出详细的解题步骤
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![已知cos(15°+a)=4/5,a为锐角,详细题目如下已知cos(15°+a)=4/5,a为锐角,求sin(435°-a)+sin(a-165°) /cos(195°+a)的值.请写出详细的解题步骤](/uploads/image/z/7199691-51-1.jpg?t=%E5%B7%B2%E7%9F%A5cos%EF%BC%8815%C2%B0%2Ba%EF%BC%89%3D4%2F5%2Ca%E4%B8%BA%E9%94%90%E8%A7%92%2C%E8%AF%A6%E7%BB%86%E9%A2%98%E7%9B%AE%E5%A6%82%E4%B8%8B%E5%B7%B2%E7%9F%A5cos%EF%BC%8815%C2%B0%2Ba%EF%BC%89%3D4%2F5%2Ca%E4%B8%BA%E9%94%90%E8%A7%92%2C%E6%B1%82sin%28435%C2%B0%EF%BC%8Da%29%2Bsin%28a%EF%BC%8D165%C2%B0%29+%EF%BC%8Fcos%28195%C2%B0%2Ba%29%E7%9A%84%E5%80%BC.%E8%AF%B7%E5%86%99%E5%87%BA%E8%AF%A6%E7%BB%86%E7%9A%84%E8%A7%A3%E9%A2%98%E6%AD%A5%E9%AA%A4)
已知cos(15°+a)=4/5,a为锐角,详细题目如下已知cos(15°+a)=4/5,a为锐角,求sin(435°-a)+sin(a-165°) /cos(195°+a)的值.请写出详细的解题步骤
已知cos(15°+a)=4/5,a为锐角,详细题目如下
已知cos(15°+a)=4/5,a为锐角,求sin(435°-a)+sin(a-165°) /cos(195°+a)的值.请写出详细的解题步骤
已知cos(15°+a)=4/5,a为锐角,详细题目如下已知cos(15°+a)=4/5,a为锐角,求sin(435°-a)+sin(a-165°) /cos(195°+a)的值.请写出详细的解题步骤
∵0°<a<90° ∴15°<a+15°<105° ∴sin(15°+a)=3/5 ∴sin(435°-a)+sin(a-165°) =sin(360°+75°-a)-sin(165°-a) =sin(90°-(15°+a))-sin(180°-(15°+a)) =cos(15°+a)-sin(15°+a) =4/5-3/5=1/5 cos(195°+a) =cos(180+15°+a) =-cos(15°+a) =-4/5 ∴原式=1/5÷(-4/5)=-1/4