Question

已知：x-2tan

a

2

+xtan²

a

2

=0，y-1+tan²

a

2

+ytan²

a

2

=0．求证：cos2a=x²+y²-2sin²a．

Answer 1

证明：∵x-2tan

a

2

+xtan²

a

2

=0∴x=

2tan α 2

1+tan2 α 2

=sinα；
∵y-1+tan²

a

2

+ytan²

a

2

=0∴y=

1-tan2 α 2

1+tan2 α 2

=cosα．
则cos2α=1-2sin²α=sin²α+cos²α-2sin²α=x²+y²-2sin²a得证