ABC is a triangle such that `sin(2A+B)=sin(C-A)=-sin(B+2C)=1/2`. If A,B, and C are in AP. then the value of A,B and C are..

Explanation

Here, `sin(B+2C) = -1/2`

As it is a negative value, `(B+2C)` is greater than `180^@` .
`:. B+2C = 180+30=> B+2C = 210^@->(1)`

`sin(C-A) = 1/2=> C-A = 30^@->(2)`

`sin(2A+B) = 1/2 => 2A+B = 180-30=>2A+B = 150^@->(3)`

As, `A,B and C` are in AP.

`:. A+C = 2B->(4)`

From (1),

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