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Question

If tanA and tanB are the roots of quadratic equation x2ax+b=0, then the value of sin2(A+B) is

A
a2a2+(1b)2
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B
a2a2+b2
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C
a2a2b2
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D
a2b2(1a)2
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Solution

The correct option is A a2a2+(1b)2
x2ax+b=0 has roots tanA,tanB
So, tanA+tanB=a
and tanAtanB=b
tan(A+B)=tanA+tanB1tanAtanBtan(A+B)=a1b

Therefore, sin2(A+B)
=1cosec2(A+B)=11+cot2(A+B)=11+(1ba)2=a2a2+(1b2)

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