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If Sin A/ Sin B = p and Cos A/ Cos B = q, find tan A and tan B |
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Answer» Step-by-step explanation: sinB sinA
=p; cosB cosA
=Q sinA=psinB−−−(1);cosA=qcosB−−−(2) TANA= q p
tanB−−−(3)(dividing(1)by(2))sinAcosA=pqsinBcosB(Multiply(1)&(2)) 2 Acos 2 sinAcosA
= cos 2 Acos 2 B pqsinBcosB
=sec 2 BtanA=pqsec 2 AtanB =(1+tan 2 B)tanA=pq(1+tan 2 A)tanB =[1+( q p
tanA) 2 ]tanA=pq(1+tan 2 A). q p
tanA(by(3)) =1+ q 2
p 2
tan 2 A=q 2 +q 2 tan 2 A =tan 2 A( p 2
q 2
−q 2 )=q 2 −1 =tan 2 A q 2 −p 2 q 2
(q 2 −1)p 2
tanA= q 2 (p 2 −1) p 2 (1−q 2 )
= q p
p 2 −1 1−q 2
tanB= p 2 −1 1−q 2
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