1、高一数学三角函数公式两角和与差的三角函数 cos(+)=coscos-sinsin cos(-)=coscos+sinsin sin()=sincoscossin tan(+)=(tan+tan)/(1-tantan) tan(-)=(tan-tan)/(1+tantan)和差化积公式 sin+sin=2sin(+)/2cos(-)/2 sin-sin=2cos(+)/2sin(-)/2 cos+cos=2cos(+)/2cos(-)/2 cos-cos=-2sin(+)/2sin(-)/2积化和差公式 sincos=(1/2)sin(+)+sin(-) cossin=(1/2)sin(+)-
2、sin(-) coscos=(1/2)cos(+)+cos(-) sinsin=-(1/2)cos(+)-cos(-)倍角公式 sin(2)=2sincos=2/(tan+cot) cos(2)=(cos)2-(sin)2=2(cos)2-1=1-2(sin)2 tan(2)=2tan/(1-tan2) cot(2)=(cot2-1)/(2cot) sec(2)=sec2/(1-tan2) csc(2)=1/2*seccsc三倍角公式 sin(3) = 3sin-4sin3 = 4sinsin(60+)sin(60-) cos(3) = 4cos3-3cos = 4coscos(60+)cos
3、(60-) tan(3) = (3tan-tan3)/(1-3tan2) = tantan(/3+)tan(/3-) cot(3)=(cot3-3cot)/(3cot2-1)n倍角公式 sin(n)=ncos(n-1)sin-C(n,3)cos(n-3)sin3+C(n,5)cos(n-5)sin5- cos(n)=cosn-C(n,2)cos(n-2)sin2+C(n,4)cos(n-4)sin4-半角公式 sin(/2)=(1-cos)/2) cos(/2)=(1+cos)/2) tan(/2)=(1-cos)/(1+cos)=sin/(1+cos)=(1-cos)/sin cot(/2)
4、=(1+cos)/(1-cos)=(1+cos)/sin=sin/(1-cos) sec(/2)=(2sec/(sec+1) csc(/2)=(2sec/(sec-1)辅助角公式 Asin+Bcos=(A2+B2)sin(+arctan(B/A) Asin+Bcos=(A2+B2)cos(-arctan(A/B)万能公式 sin(a)= (2tan(a/2)/(1+tan2(a/2) cos(a)= (1-tan2(a/2)/(1+tan2(a/2) tan(a)= (2tan(a/2)/(1-tan2(a/2)降幂公式 sin2=(1-cos(2)/2=versin(2)/2 cos2=(1
5、+cos(2)/2=covers(2)/2 tan2=(1-cos(2)/(1+cos(2)三角和的三角函数 sin(+)=sincoscos+cossincos+coscossin-sinsinsin cos(+)=coscoscos-cossinsin-sincossin-sinsincos tan(+)=(tan+tan+tan-tantantan)/(1-tantan-tantan-tantan)其它公式 1+sin(a)=(sin(a/2)+cos(a/2)2 1-sin(a)=(sin(a/2)-cos(a/2)2 csc(a)=1/sin(a) sec(a)=1/cos(a) cos30=sin60 sin30=cos60推导公式 tan+cot=2/sin2 tan-cot=-2cot2 1+cos2=2cos2 1-cos2=2sin2 1+sin=sin(/2)+cos(/2)2
