Question

若角α的终边在直线y=2x上，则

sin(1800-α)+cos(1800-α)

sin(900+α)+cos(900-α)

=______．

Answer 1

因为角α的终边在直线y=2x上，所以tanα=2，
则

sin(1800-α)+cos(1800-α)

sin(900+α)+cos(900-α)

=

sinα-cosα

cosα+sinα

=

tanα-1

1+tanα

=

2-1

1+2

=

1

3

．
故答案为：

1

3