题目内容
已知0<β<
<α<π,且
,
,
求cos(α+β)的值.
∵0<β<
<α<π,∴-
<
-β<
,
<α-
<π,
∴cos
=
=
,sin
=
=
,
∴cos
=cos![]()
=cos
cos
+sin
sin![]()
=
×
+
×
=
,∴cos(α+β)=2cos2
-1=2×
-1=-
.
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题目内容
已知0<β<
<α<π,且
,
,
求cos(α+β)的值.
∵0<β<
<α<π,∴-
<
-β<
,
<α-
<π,
∴cos
=
=
,sin
=
=
,
∴cos
=cos![]()
=cos
cos
+sin
sin![]()
=
×
+
×
=
,∴cos(α+β)=2cos2
-1=2×
-1=-
.