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

1.	In a triangle ABC, if `2b=a+c` and `A-C=90`, then `sin B` equals
Answer» 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)` So, `sin(B)=2sin(B/2)cos(B/2)=2sqrt7/(4*2)=sqrt7/4`

Discussion

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