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If Tan A/2 and Tan B/2 are the roots of the equation 8x^2 – 26x +15 = 0 then cos(A+B) =?

If Tan A/2 and Tan B/2 are the roots of the equation 8x^2 – 26x +15 = 0 then cos(A+B) =?

Grade:11

1 Answers

Arun
25758 Points
4 years ago
Dear student
 
tan A/2 + tan B/2 = 26/8 = 13/4
tan A/2 * tanB/2 = 15/8
 
Thus tan(A+B/2) = -26/7 (from formula)
 
Now 
Cos(A+ B) = [1 - tan²(A+B/2)] /[1 + tan² (A+B/2)]
 
Cos (A+B) = -627/725
 
Regards
Arun (askIITians forum expert)

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