a属于{π,π/2}.tan(a+ π/4)=1/7,求sina+ cosa等于多少?

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a属于{π,π/2}.tan(a+ π/4)=1/7,求sina+ cosa等于多少?
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a属于{π,π/2}.tan(a+ π/4)=1/7,求sina+ cosa等于多少?
a属于{π,π/2}.tan(a+ π/4)=1/7,求sina+ cosa等于多少?

a属于{π,π/2}.tan(a+ π/4)=1/7,求sina+ cosa等于多少?
tan(a+π/4)=(tana+tanπ/4)/(1-tanatanπ/4)=1/7
7tana+7=1-tana
tana=sina/cosa=-3/4
sina=-3cosa/4
sin²a=9cos²a/16
sin²a+cos²a=1
所以cos²a=16/25,sin²a=9/25
a在第二象限则cosa=-4/5,sina=3/5
所以原式=-1/5