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a 1 a 2 a 3 a 4 are the roots of the roots of the equation sin(A + B) = ksin2a, no two of which differ by a multiple of 2 π, then a 1 + a 2 + a 3 + a 4 is equal to?

a1 a2 a3 a4  are the roots of the roots of the equation sin(A + B) = ksin2a, no two of which differ by a multiple of 2π, then a1 + a2 + a3 + a4  is equal to?
 
 

Grade:11

1 Answers

Ravi
askIITians Faculty 69 Points
6 years ago
Expand the LHS and solve for A and B so as to attain the RHS trigonometric ratio, which in this case is Sin2a.

4 values as multiples of an angle would fall in the range of 0,2π corresponding to the values of a1, a2......... Add them to get the final answer.

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