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# suppose the sum of 2 angles A and B =Cwhere C is between -90 to 90so      A + B = C$\Rightarrow$ sin(A+B) = sinC$\Rightarrow$ sin(A+B) =sin (180-C)$\Rightarrow$ A + B = 180 – C$\Rightarrow$ A + B + C = 180plz tell me my mistake as we all know that this thing is not at all true

Ajay
209 Points
4 years ago
Posting again as some errors in previois answer

sin x = sin y implies x = nπ + (– 1)n y, where n ∈ Z.

in Your case Sin (A+B) = Sin(180-C) implies
A+B = 180-C for n = 0
This solution is not correct as explained
Since C -90 implies 180-C  > 90.
But A+B  = C is less than 90 hence this solution is discarded

The correct solution to this equation is
A+B = 180 – (180-C)  = C for n  =1