sin(A+π/4)=7√2/10 A∈(π/4,π/2) 求 cosA的值.我的算法,请大侠指点.sinAcosπ/4+sinπ/4cosA=7√2/10 sinA+cosA=7/5然后怎么办大侠别省你们的过程,
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sin(A+π/4)=7√2/10 A∈(π/4,π/2) 求 cosA的值.
我的算法,请大侠指点.sinAcosπ/4+sinπ/4cosA=7√2/10
sinA+cosA=7/5
然后怎么办大侠别省你们的过程,
sinA+cosA=7/5
平方得
(sinA+cosA)²=(7/5)²
sin²A+2sinAcosA+cos²A=49/25
2sinAcosA+1=49/25
sinAcosA=12/25
则sinA cosA是方程
x²-(7/5)x+12/15=0两根
(x-3/5)(x-4/5)=0
x=3/5或4/5
即
cosA=3/5或4/5
sinA+cosA=7/5 -> sinA=7/5-cosA
sinA^2+cosA^2=1
(7/5-cosA)^2+cosA^2=1
25cosA^2-35cosA+12=0
因为A∈(π/4,π/2)
所以0
A∈(π/4,π/2)
A+π/4∈(π/2,3π/4)
cos(A+π/4)= -1/5√2
cosA
=cos(A+π/4-π/4)
=cos(A+π/4)cosπ/4+sin(A+π/4)sinπ/4
=-1/5√2(√2/2)+7√2/10(√2/2)
=3/5
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