已知cos（15°+α）=3/5，α为锐角，求：tαn(435°−α)+sin(α−165°)cos(195°+α)×sin(105°+α)．

题目

已知cos（15°+α）=

3

5

答案

∵cos（15°+α）=

3

5

，α为锐角，
∴sin（15°+α）=

4

5

，
∴cot（15°+α）=

cos(15°+α)

sin(15°+α)

=

3

4

．
∴

tαn(435°−α)+sin(α−165°)

cos(195°+α)×sin(105°+α)

=

tan(75°−α)−sin(α+15°)

−cos(15°+α)•cos(15°+α)

=

cot(15°+α)−sin(15°+α)

−cos2(15°+α)

=

3 4  − 4 5

−( 3 5 )2

=

20

9

-

25

12

=

5

36

．