tan(α+45°)
=(tanα+1)/(1-tanα)=2
tanα+1=2-2tanα
tanα=1/3
即sinα/cosα=1/3
cosα=3sinα
而sin²α+cos²α=sin²α+9sin²α=10sin²α=1
所以sin²α=0.1
原式=(1+3sinα)[cosα-2(1-2sin²α)]
=(1+3sinα)(3sinα-2+4sin²α)
=(1+3sinα)(3sinα-1.6)
=9sinα²-1.8sinα-1.6
= -1.8sinα-0.7
当sinα=√10/10时,原式= -7/10-9√10 /50
当sinα=-√10/10时,原式=-7/10+9√10/50