三角函数化简问题
\u4e09\u89d2\u51fd\u6570\u5316\u7b80\u9898tan10-\u221a3
=sin10/cos10-\u221a3
=(sin10-\u221a3cos10)/cos10
=2sin(10-60)/cos10
=-2sin50/cos10
sin40(tan10-\u221a3\uff09
=-(2sin40sin50)/cos10
=-[cos(50-40)-cos(50+40)]/cos10
=-cos10/cos10
=-1
tan70\u00b0cos10\u00b0[SQR(3)tan20\u00b0\u20141]
=(cot20)cos10[(\u6839\u53f73)tan20\u00b0-1]
=(\u6839\u53f73)cos10-(cot20)cos10
=(\u6839\u53f73)cos10-(cos20/sin20)cos10
=(\u6839\u53f73)cos10-cos20/(2sin10)
={2\u500d(\u6839\u53f73)sin10cos10-cos20}/(2sin10)
=[(\u6839\u53f73)sin20-cos20]/(2sin10)
=2sin(20-30)/2sin10
=-2sin10/2sin10
=-1
sin50(1+\u221a3tan10)
=sin50[1+(\u221a3sin10/cos10)]
=sin50[cos10+\u221a3sin10)/cos10]
=2sin50[(1/2)cos10+(\u221a3/2)sin10)/cos10]
=2sin50[cos60cos10+sin60sin10)/cos10]
=2sin50cos(60-10)/cos10
=2sin50cos50/cos10
=sin100/cos10
=cos10/cos10
=1
\u89e3\u30102sin50º+sin10º(1+\u221a3 tan10º)\u3011\u00d7\u221a\uff08sin²80º\uff09
=\u30102sin50º+sin10º(1+\u221a3 sin10º/cos10\u00b0)\u3011\u00d7\u221a\uff08sin²80º\uff09
=\u30102sin50º+sin10º(cos10\u00b0/cos10\u00b0+\u221a3 sin10º/cos10\u00b0)\u3011\u00d7sin80º
=\u30102sin50º+sin10º(\uff08cos10\u00b0+\u221a3 sin10º\uff09/cos10\u00b0)\u3011\u00d7sin80º
=\u30102sin50º+sin10º(2\uff081/2cos10\u00b0+\u221a3 /2sin10º\uff09/cos10\u00b0)\u3011\u00d7sin80º
=\u30102sin50º+sin10º(2\uff08sin30\u00b0cos10\u00b0+cos30\u00b0sin10º\uff09/cos10\u00b0)\u3011\u00d7sin80º
=\u30102sin50º+2*sin10º*sin40\u00b0/cos10\u00b0\u3011\u00d7sin80º
=2\u3010sin50ºcos10\u00b0/cos10\u00b0+sin10º*sin40\u00b0/cos10\u00b0\u3011\u00d7sin80º
=2\u3010\uff08sin50ºcos10\u00b0+sin10º*sin40\u00b0\uff09/cos10\u00b0\u3011\u00d7sin80º
=2\u3010\uff08sin50ºcos10\u00b0+sin10º*cos50\u00b0\uff09/cos10\u00b0\u3011\u00d7sin80º
=2\u3010\uff08sin60º/cos10\u00b0\u3011\u00d7sin80º
=2\u3010\uff08sin60º/cos10\u00b0\u3011\u00d7cos10\u00b0
=2sin60º
=\u221a3
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