三角恒等變形公式大全

1、和角差角:cos(±=coscos干sinsinsin(±=sincos±cossintan(±=(tan±tan/(1干tantan二倍角公式:sin(2=2sincos=2tan2(/1+tan2( cos(2=cos2(-sin2(=2cos2(-1=1-2sin2(=(1-tan2(/(1+tan2( tan(2=2tan/1-tan2(半角公式:sin2(/2=(1-cos/2cos2(/2=(1+cos/2tan2(/2=(1-cos/(1+costan(/2=sin/(1+cos=(1-cos/sin三倍角公式:sin3=3sin

2、-4sin3(cos3=4cos3(-3costan3=(3tan-tan3(÷(1-3tan2(sin3=4sin×sin(60-sin(60+cos3=4cos×cos(60-cos(60+tan3=4tan×tan(60-tan(60+萬能代換公式:半角的正弦、余弦和正切公式(降冪擴角公式 sin=2tan(/2/1+tan2(/2cos=1-tan2(/2/1+tan2(/2tan=2tan(/2/1-tan2(/2積化和差公式:sin·cos=(1/2sin(+sin(-cos·sin=(1/2sin(+-sin(-cos&

3、#183;cos=(1/2cos(+cos(-sin·sin=-(1/2cos(+-cos(-和差化積公式:sin+sin=2sin(+/2cos(-/2sin-sin=2cos(+/2sin(-/2cos+cos=2cos(+/2cos(-/2cos-cos=-2sin(+/2sin(-/2和角差角:cos(±=coscos干sinsinsin(±=sincos±cossintan(±=(tan±tan/(1干tantan二倍角公式:sin(2=2sincos=2tan2(/1+tan2( cos(2=cos2(-sin2(=2co

4、s2(-1=1-2sin2(=(1-tan2(/(1+tan2( tan(2=2tan/1-tan2(半角公式:sin2(/2=(1-cos/2cos2(/2=(1+cos/2tan2(/2=(1-cos/(1+costan(/2=sin/(1+cos=(1-cos/sin三倍角公式:sin3=3sin-4sin3(cos3=4cos3(-3costan3=(3tan-tan3(÷(1-3tan2(sin3=4sin×sin(60-sin(60+cos3=4cos×cos(60-cos(60+tan3=4tan×tan(60-tan(60+萬能代換公式:

5、半角的正弦、余弦和正切公式(降冪擴角公式 sin=2tan(/2/1+tan2(/2cos=1-tan2(/2/1+tan2(/2tan=2tan(/2/1-tan2(/2 積化和差公式:sin·cos=(1/2sin(+sin(-cos·sin=(1/2sin(+-sin(-cos·cos=(1/2cos(+cos(-sin·sin=-(1/2cos(+-cos(-和差化積公式:sin+sin=2sin(+/2cos(-/2sin-sin=2cos(+/2sin(-/2cos+cos=2cos(+/2cos(-/2cos-cos=-2sin(+/2si

6、n(-/2和角差角:cos(±=coscos干sinsinsin(±=sincos±cossintan(±=(tan±tan/(1干tantan二倍角公式:sin(2=2sincos=2tan2(/1+tan2( cos(2=cos2(-sin2(=2cos2(-1=1-2sin2(=(1-tan2(/(1+tan2( tan(2=2tan/1-tan2(半角公式:sin2(/2=(1-cos/2cos2(/2=(1+cos/2tan2(/2=(1-cos/(1+costan(/2=sin/(1+cos=(1-cos/sin三倍角公式:sin3

7、=3sin-4sin3(cos3=4cos3(-3costan3=(3tan-tan3(÷(1-3tan2(sin3=4sin×sin(60-sin(60+cos3=4cos×cos(60-cos(60+tan3=4tan×tan(60-tan(60+萬能代換公式:半角的正弦、余弦和正切公式(降冪擴角公式 sin=2tan(/2/1+tan2(/2cos=1-tan2(/2/1+tan2(/2tan=2tan(/2/1-tan2(/2積化和差公式:sin·cos=(1/2sin(+sin(-cos·sin=(1/2sin(+-sin(

8、-cos·cos=(1/2cos(+cos(-sin·sin=-(1/2cos(+-cos(-和差化積公式:sin+sin=2sin(+/2cos(-/2sin-sin=2cos(+/2sin(-/2cos+cos=2cos(+/2cos(-/2cos-cos=-2sin(+/2sin(-/2和角差角:cos(±=coscos干sinsinsin(±=sincos±cossintan(±=(tan±tan/(1干tantan二倍角公式:sin(2=2sincos=2tan2(/1+tan2( cos(2=cos2(-sin2(=2cos2(-1=1-2s