Question

已知sinα+cosα/sinα-cosα=2,求sin^2-2sinαcosα+1的值

Answer 1

sinα+cosα/sinα-cosα=2
分子分母同时处以cosa得
(tana+1)/(tana-1)=2
tana+1=2tana-2
tana=3

sin²a-2sinacosa+1
=(sin²a-2sinacosa+sin²a+cos²a)/(sin²a+cos²a)
=(2sin²a-2sinacosa+cos²a)/(sin²a+cos²a)
分子分母同时处以cos²a得
=(2tan²a-2tana+1)/(tan²a+1)
带入 tana=3得
=(18-6+1)/(9+1)
=13/10

Answer 2

sina=3cosa
sin^2a=9/10
sin^2a-2sinacosa+1=9/10-2/3*sin^2a+1=9/10-6/10+1=13/10