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Question

If tanA and tanB are the roots of the quadratic equation, 3x210x25=0, then the value of 3sin2(A+B)10sin(A+B)cos(A+B)25cos2(A+B) is :

A
10
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B
10
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C
25
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D
25
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Solution

The correct option is C 25
3x210x25=03x215x+5x25=0(3x+5)(x5)=0x=53, 5
Now,
tan(A+B)=tanA+tanB1tanAtanB =5531+253=514cos(A+B)=14221
Now,
S=3sin2(A+B)10sin(A+B)cos(A+B)25cos2(A+B)S=cos2(A+B)[3tan2(A+B)10tan(A+B)25]S=196221[3×2519610×51425]S=25221[328196]S=25

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