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In a triangle ABC, if 2b=a+c and A-C=90,...

In a triangle ABC, if `2b=a+c` and `A-C=90`, then `sin B` equals

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As, 2b=a+c
So by sine rule, `2sinB=sinA + sinC`
`2sinB=2sin((A+C)/2)cos((A-C)/2)` `sinB=sin((pi-B)/2)cos(pi/4)` `2sin(B/2)cos(B/2)=cos(B/2)*(1/sqrt2)` `sin(B/2)=1/(2sqrt2)`
Hence, `cos(B/2)=sqrt7/(2sqrt2)`
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