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In a DeltaABC,(a+c)/(a-c)tanB/2 is equa...

In a `DeltaABC,(a+c)/(a-c)tanB/2` is equal to

A

`tan(B/2+C)`

B

`tan(B+C/2)`

C

`cot(B/2+C)`

D

none of these

Text Solution

Verified by Experts

Using sine rule, we have
`(a+c)/(a-c)tanB/2=(sinA+sinC)/(sinA-sinC)tanB/2`
`rArr(a+c)/(a-c)tanB/2=(2sin(A+C)/2cos(A-C)/2)/(2sin(A-C)/2cos(A+C)/2)tanB/2`
`rArr(a+c)/(a-c)tanB/2=(cosB/2cos(A-C)/2)/(sin(A-C)/2sinB/2)tanB/2`
`rArr(a+c)/(a-c)tanB/2=(cosB/2cos(A-C)/2)/(sin(A-C)/2sinB/2).tanB/2`
`rArr(a+c)/(a-c)tanB/2=cot((A-C)/2)`
`rArr(a+c)/(a-c)tanB/2=cot((A-C)/2)`
`rArr(a+c)/(a-c)tanB/2=cot((pi-B-C-C)/2)[becauseA+B+C=pi]`
`rArr(a+c)/(a-c)tanB/2=tan(B/2+C)`
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Knowledge Check

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    A
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    B
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    B
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    C
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    D
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