Question

（2010•南京三模）已知A为锐角，sinA＝35，tan(A−B)＝−12，求cos2A及tanB的值．

Answer 1

cos2A=1-2sin²A=1-[9/25]×2=[7/25]

∵A为锐角，sinA=[3/5]

∴tanA=

sinA

1−sin2A=[3/4]

∴tanB=tan[A-（A-B）]=

tanA−tan(A−B)

1+tanAtan(A−B)=

3

4+

1

2

1−

3

4×

1

2=2