x为锐角,sin(x+15°)=4/5,则cos(2x-15°)=?
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x为锐角,sin(x+15°)=4/5,则cos(2x-15°)=?
2x-15=2(x+15)-45
因为sin(x+15°)=4/5
所以cos(x+15°)=3/5
sin(2x+30°)=2*4/5*3/5=24/25
cos(2x+30°)=-7/25
故cos(2x-15°)=cos((2x+30°)-45)=cos(2x+30°)cos45+sin(2x+30°)sin45
=-7/25cos45+24/25sin45=17√2/50
因为sin(x+15°)=4/5
所以cos(x+15°)=3/5
sin(2x+30°)=2*4/5*3/5=24/25
cos(2x+30°)=-7/25
故cos(2x-15°)=cos((2x+30°)-45)=cos(2x+30°)cos45+sin(2x+30°)sin45
=-7/25cos45+24/25sin45=17√2/50
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