题目内容
化简下列各式:(1)cos(80°+3α)cos(35°+3α)+sin(80°+3α)cos(55°-3α);
(2)sin(x+
)+2sin(x-
)-
cos(
-x);
(3)
.
解析:(1)原式=cos(80°+3α)cos(35°+3α)+sin(80°+3α)sin(35°+3α)
=cos［(80°+3α)-(35°+3α)］=cos45°=.
(2)原式=sinxcos+cosxsin+2sinxcos-2cosxsin-
cos
cosx-
sin
sinx
=
sinx-
cosx+
cosx-
sinx=0.
(3)原式=
=
=tan(α-β).
答案:(1)
;(2)0;(3)tan(α-β).
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