Question

設角α=-

35

6

π，則

2sin(π+α)cos(π-α)-cos(π+α)

1+sin2α+sin(π-α)-cos2(π+α)

的值等于（　　）

A． 3 3

B．- 3 3

C． 3

D．- 3

Answer 1

因為α=-

35

6

π，
則

2sin(π+α)cos(π-α)-cos(π+α)

1+sin2α+sin(π-α)-cos2(π+α)

=

2sinαcosα+cosα

1+sinα- cos2α

=

sin2α+cosα

1+sinα-cos2α

=

-sin 35 3 π+cos 35 6 π

1-sin 35 6 π-cos 35 3 π

=

-sin(12π- 1 3 π)+cos(6π- 1 6 π)

1-sin(6π- 1 6 π)-cos(12π- 1 3 π)

=

sin π 3 +cos π 6

1+sin π 6 -cos π 3

=

3

．
故選C