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Grade 12Trigonometry

The question is (a square-b square)sinAsinB divided by two sin( A-B) is equal to

Question image for The question is (a square-b square)sinAsinB divide
Profile image of Nirmal Aditya
8 Years agoGrade 12
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1 Answer

Profile image of Harshit
8 Years ago
= (a2-b2)sinAsinB/2sin(A-B)
= (a2-b2) ab/ 4R2 2sin(A-B)     [a/sinA=b/sinB=2R]
= (a2-b2) ab/ 4R2 [sinAcosB-sinBcosA]
= (a2-b2) ab/ 4R2 [a(a2+c2-b2)/ 2R(2ac) – b (b2+c2-a2)/ 2R(2bc)]
=(a2-b2) ab/ R [(a2+c2-b2)- (b2+c2-a2)/c]
=(a2-b2) abc/ R [2(a2-b2)]
= abc/2R      [abc=4Rdelta]
 = 2delta
 so the answer is 2 delta

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