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Question

# If tan A and tan B are the roots of the quadratic equation x2 -ax+b=0, then the value of sin2 (A+B) is

A

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B

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C

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D

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Solution

## The correct option is A We want to find sin2 (A+B). If we know tan (A+B) or cos (A+B) or sin (A+B) or any other basic trigonometric ratio of the angle A+B, we can find sin2 (A+B) easily. Since we are given tanA and tanB are the roots of a quadratic education, we can find tanA+tanB and tanAtanB. Once we have these two, we can find tan (A+B). TanA+tanB = a TanAtanB = b ⇒ tan (A+B) = tanA+tanB1−tanAtanB = a1−b We will construct a △ and proceed Sin (A+B) = a√a2+(1−b)2 ⇒sin2(A+B)=a2a2+(1−b)2 Key steps/concepts : (1) Finding tan (A+B)

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