Question

已知sinα是方程5x²-7x-6=0的根，求

sin(-α- 3 2 π)•sin( 3 2 π-α)•tan2(2π-α)

cos( π 2 -α)•cos( π 2 +α)•cos2(π-α)

的值．

Answer 1

∵sinα是方程5x²-7x-6=0的根，∴sinα=-

3

5

或sinα=2（舍）．
故sin²α=

9

25

，cos²α=

16

25

?tan²α=

9

16

．
∴原式=

cosα•(-cosα)•tan2α

sinα•(-sinα)•cos2α

=

cosα•(-cosα)• sin2α cos2α

sinα•(-sinα)•cos2α

=

1

cos2α

=sec²α=1+tan²α=1+

9

16

=

25

16