Question

化简：（1）?sin(180°+α)+sin(?α)?tan(360°+α)tan(α+180°)+cos(?α)+cos(180°?α)（2）sin120°?

化简：（1）?sin(180°+α)+sin(?α)?tan(360°+α)tan(α+180°)+cos(?α)+cos(180°?α)（2）sin120°?cos330°+sin（-690°）cos（-660°）+tan675°+cot765°．

Answer 1

（1）原式=

sinα?sinα?tanα

tanα+cosα?cosα

=

?tanα

tanα

=-1；
（2）原式=sin120°cos（360°-30°）-sin（720°-30°）cos（-720°+60°）+tan（720°-45°）+

1

tan(720°+45°)

=

3

2

×

3

2

+

1

2

×

1

2

-1+1=1．