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

问题描述:

已知cos(15°+α)=

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

∵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