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Let A, B. C be three angles such that A ...

Let A, B. C be three angles such that `A =pi/4`. and `tan B tan C= P` . Find all possible values of P such A, B, C are angles of a triangle

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`A+B+C=pi`
`B+c=pi-pi/4`
`B+C=3/4pi`
`0<=B,C<=3/4pi`
`tanB*tanC=P`
`sinB/cosB*sinC/cosC=P/1`
`(sinBsinC+cosBcosC)/(sinBsinC-cosBcosC)=(P+1)/(P-1)`
`(cos(B-C))/(-cos(B+C))=(P+1)/(P-1)`
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