问题 解答题
已知cos
x
2
+2sin
x
2
=0

(Ⅰ)求tanx的值;
(Ⅱ)求
cos2x
2
sin(
π
4
+x)•cosx
的值.
答案

cos

x
2
+2sin
x
2
=0解得tan
x
2
=-
1
2

(1)tanx=

2tan
x
2
1-(tan
x
2
)
2
=
-
1
2
×2
1-
1
4
=-
4
3

(2)

cos2x
2
sin(
π
4
+x)•cosx
=
cos2x-sin2x
sinxcosx+cos2x
=
1-tan2x
tanx+1
=
1+
4
3
-
4
3
+1
=-7

填空题
单项选择题