已知函数f(x)=2sinxcosx+cos2x(Ⅰ)求f(π4)的值;(Ⅱ)设α∈(0,π),f(α2)=22,求sinα的值

2025-06-27 15:30:47
推荐回答(1个)
回答1:

(Ⅰ)∵f(x)=sin2x+cos2x
f(

π
4
)=sin
π
2
+cos
π
2
=1
(Ⅱ)f(
α
2
)=cosα+sinα=
2
2

sin(α+
π
4
)=
1
2
,cos(α+
π
4
)=±
3
2
sinα=sin(α+
π
4
?
π
4
)=
1
2
×
2
2
?
3
2
×
2
2
2
?