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Question

Find the acute angles A and B satisfying

(a) cot(A+B)=1, cosec(AB)=2

(b) secA cotB secA2 cotB+2=0

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Solution

(a)
cot(A+B)=1,cosec(AB)=2A+B=π4,AB=π6
Adding two equations,
A+B+AB=π4+π62A=10π24A=5π24andB=π45π24=π24
(b)
secAcotBsecA2cotB+2=0secA(cotB1)2(cotB1)=0(secA2)(cotB1)=0secA2=0,cotB1=0secA=2,cotB=1A=π3,B=π4




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