tan(a+b)=3,tan(a-b)=5,求tan2a和tan2b的值_数学解答

tan(a+b)=3,tan(a-b)=5,求tan2a和tan2b的值

人气：359 ℃　时间：2020-07-13 22:33:49

解答

[[1]]
tan(2a)
=tan[(a+b)+(a-b)]
=[tan(a+b)+tan(a-b)]/[1-tan(a+b)tan(a-b)]
=(3+5)/(1-3×5)
=8/(-14)
=-4/7
[[2]]
tan(2b)
=tan[(a+b)-(a-b)]
=[tan(a+b)-tan(a-b)]/[1+tan(a+b)tan(a-b)]
=(3-5)/(1+3×5)
=-2/16
=-1/8