Question

化简：（1）sin120°cos（-30°）+cos60°sin（-1050°）；（2）cos(?π2+α)sin(2π+α)cos(π+α)cos(7

化简：（1）sin120°cos（-30°）+cos60°sin（-1050°）；（2）cos(?π2+α)sin(2π+α)cos(π+α)cos(7π2?α)cos(π?α)sin(?π?α)sin(3π?α)sin(15π2+α)．

Answer 1

（1）sin120°cos（-30°）+cos60°sin（-1050°）=

3

2

×

3

2

?

1

2

×

1

2

=

1

2

；
（2）

cos(? π 2 +α)sin(2π+α)cos(π+α)cos( 7π 2 ?α)

cos(π?α)sin(?π?α)sin(3π?α)sin( 15π 2 +α)

=

sinαsinαcosαsinα

cosαsinαsinαcosα

=1．