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In any Delta A B C , the value of 2a csi...

In any `Delta A B C` , the value of `2a csin((A-B+C)/2)` is (a)`a^2+b^2-c^2` (b) `c^2+a^2-b^2` (c) `b^2-c^2-a^2` (d) `c^2-a^2-b^2`

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In `△ABC,A+B+C=180^@ ..... (i)`
GIven, `2acsin((A−B+C​)/2) `
=`2acsin((180^@−2B​)/2) `..... From (i)
=`2acsin(90^o−B) `
=`2ac cosB ...... [∵sin(90−x)=cosx]`
=`a^2+c^2−b^2`[By cosine law `2ac cosB=a^2+c^2−b^2]`
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