(2010•哈尔滨模拟)已知sin(x+π4)=−34
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(2010•哈尔滨模拟)已知sin(x+
)=−
π |
4 |
3 |
4 |
![(2010•哈尔滨模拟)已知sin(x+π4)=−34](/uploads/image/z/8695240-16-0.jpg?t=%EF%BC%882010%E2%80%A2%E5%93%88%E5%B0%94%E6%BB%A8%E6%A8%A1%E6%8B%9F%EF%BC%89%E5%B7%B2%E7%9F%A5sin%28x%2B%CF%804%29%EF%BC%9D%E2%88%9234)
解法1:由题中的条件得
2
2(sinx+cosx)=-
3
4,
两边平方得
1
2(1+2sinxcosx)=
9
16,
解得sinxcosx=
1
16
则sin2x=2sinxcosx=2×
1
16=
1
8;
解法2:sin2x=-cos2(x+
π
4)=-[1-2sin2(x+
π
4)]=
1
8.
故答案为:
1
8
2
2(sinx+cosx)=-
3
4,
两边平方得
1
2(1+2sinxcosx)=
9
16,
解得sinxcosx=
1
16
则sin2x=2sinxcosx=2×
1
16=
1
8;
解法2:sin2x=-cos2(x+
π
4)=-[1-2sin2(x+
π
4)]=
1
8.
故答案为:
1
8
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