问题 填空题
已知
a
=(-sint,cost),
b
=(1,-t),
a
b
,则(1+t2)(1+cos2t)-2的值为______.
答案

因为

a
=(-sint,cost),
b
=(1,-t)

a
b
,得:-sint×1+(-t)×cost=0,

所以sint+tcost=0,cos2t=

sin2t
t2

(1+t2)(1+cos2t)-2=2(1+t2)cos2t-2

=2(1+t2)

sin2t
t2
-2=
2sin2t
t2
+2sin2t-2.

故答案为

2sin2t
t2
+2sin2t-2.

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