Question

已知tana=2 求（sin2a-cos2a)/(1+cot^2 a)

写个详细的过程啊

Answer 1

解：
（sin2a-cos2a)/(1+cot^2 a)
=[2tana/(1+tan^2a)-(1-tan^2a)/(1+tan^2a)]/[1+(1/tan^2a)]
将tana=2带入得
原式=[(2*2)/(1+4)-(1-4)/(1+4)]/(1+1/4)
=(4/5+3/5)/(5/4)
=7/5÷5/4
=28/25

sin2a=2tana/(1+tan^2a)
cos2a=(1-tan^2a)/(1+tan^2a)(切化弦)