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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+tanB1tanAtanB

= a1b

We will construct a and proceed

Sin (A+B) = aa2+(1b)2
sin2(A+B)=a2a2+(1b)2

Key steps/concepts : (1) Finding tan (A+B)


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