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In DeltaABC, if 2b =a+ c and A-C=90^(@),...

In `DeltaABC,` if `2b =a+ c and A-C=90^(@),` then sin B equal
All symbols used have usual meaning in `Delta ABC.]`

A

`(sqrt7)/5`

B

`(sqrt5)/8`

C

`(sqrt7)/4`

D

`(sqrt5)/3`

Text Solution

Verified by Experts

We have,
`2b=a+c`
`rArr2b=a+c` `[because a/(sinA)=b/(sinB)=c/(sinC)=k]`
`rArr2ksinB=ksinA+ksinC`
`rArr2(2sinB/2cosB/2)=2sin(A+C)/2cos(A-C)/2`
`rArr4sinB/2cosB/2=2cosB/2cos(A-C)/2`
`rArr2sinB/2=cos(A-C)/2`
`rArr2sinB/2=cos45^(@)` `[becauseA-C=90^(@)` (given)`]`
`rArrsinB/2=1/(2sqrt2)`
`rArrcosB/2=(sqrt7)/(2sqrt2)`
Hence,sinB`=2sinB/2cosB/2=(sqrt7)/4`
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