Question

已知sina+cosa/sina-cosa=2,计算下列各式的值（1）3sina+cosa/2sina+3cosa(2)？

Answer 1

sina+cosa/sina-cosa=2
分子分母同时除以cosa
(tana+1)/(tana-1)=2
∴ tana=3
(1)3sina+cosa/2sina+3cosa
分子分母同时除以cosa
=(3tana+1)/(2tana+3)
=(3*3+1)/(2*3+3)
=10/9
(2)sin^a-2sinacosa+1
=(sin^a-2sinacosa)/(sin²a+cos²a)+1
分子分母同时除以cos²a
=(tan²a-2tana)/(tan²a+1) +1
=(9-6)/(9+1)+1
=3/10+1
=13/10,8,已知sina+cosa/sina-cosa=2,计算下列各式的值（1）3sina+cosa/2sina+3cosa(2)sin^a-2sinacosa+1.