问题
解答题
化简求值 ①tan70°cos10°(
②已知sin(α+
|
答案
①tan70°cos10°(
tan20°-1)3
=cot20°cos10°(
-1)
sin20°3 cos20°
=cot20°cos10°(
)
sin20°-cos20°3 cos20°
=
×cos10°×(cos20° sin20°
)2(
sin20°-3 2
cos20°)1 2 cos20°
=
×cos10°×(cos20° sin20°
)2sin(20°-30°) cos20°
=
×(-cos20° sin20°
)sin20° cos20°
=-1
②∵sin(α+
)+sinα=-π 3
,4 3 5
∴
sinα+1 2
cosα+sinα=-3 2 4 3 5
即
sin(α+3
)=-π 6 4 3 5
∴sin(α+
)=-π 6
,又∵-4 5
<α<0,π 2
∴cos(α+
)=π 6 3 5
∴cosα=cos(α+
-π 6
)=π 6
cos(α+3 2
)+π 6
sin(α+1 2
)=π 6
×3 2
+3 5
×(-1 2
)=4 5 3
-43 10