doubt

If sin(a+b)sin(a-b)=sin c (2sin b+sin c) , 0 <a,b,c < Pi, then the family of lines xsin a+y sin b+ sin c = 0, passes through the fixed point?

1 Answers

Simplify and we get:
sin²a-sin²b=sinc(2sinb+sinc)
rearranging we get:
sin²a=(sinb+sinc)²

therefore the point is:
(-1,1) [note that (1,1) will not satisfy since 0<a,b,c<Ï€]

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