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in Trigonometry by (46.9k points)
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If tan α and tan β are the roots x2 + ax + b = 0, then sin(α + β)/sin α sin β is equal to .....

(a) c

(b) a/b

(c) a

(d) c/d

1 Answer

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Best answer

(b) a/b

tan2 x + a tan x + b = 0 

α and β are the roots of the equation 

⇒ tan2 α + a tan α + b = 0 ….. (1) 

tan2 β + a tan β + b = 0 …… (2) 

(1) – (2) => tan2 α – tan2 β + a (tan α – tan β) = 0 

(tan α – tan β) (tan α + tan β) + a (tan α – tan β) = 0 

⇒ tan α + tan β = – a …. (A)

(1) × tan β – (2) × tan α

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