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A level maths help - trigonometry

The question says to prove cosec(pi - x) can be written as cosec(x). The answer shows them turning cosec(pi - x) into 1 over sin(pi - x) and then they just turned that into 1 over sin(x). How does 1/(sin(pi-x)) turn into 1/(sin(x))? Could someone explain this to me? Thanks

Reply 1

mqb2766

Original post by earthworm206

cosec(z) = 1/sin(z) by definition.
sin(pi-x) = sin(x) by sketching the curve and eyeballing it or better using the
sin(a+b) = ...
Trig formula where a=pi and b=-x.