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)=
,α为锐角,求:3 5
. tαn(435°−α)+sin(α−165°) cos(195°+α)×sin(105°+α)
答
∵cos(15°+α)=
,α为锐角,3 5
∴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 −(
)23 5
-20 9
=25 12
.5 36