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Conisder x = 4 tan^(-1)((1)/(5)),y = tan...

Conisder x = 4 `tan^(-1)((1)/(5)),y = tan^(-1)((1)/(70))and z = tan^(-1)((1)/(99))`.
What is x - y equal to ?

A

`tan^(-1)((828)/(845))`

B

`tan^(-1)((8287)/(8450))`

C

`tan^(-1)((8281)/(8450))`

D

`tan^(-1)((8287)/(8471))`

Text Solution

Verified by Experts

The correct Answer is:
C
`x-y=tan^(-1)((120)/(119))-"tan"^(-1)(1)/(70)`
`=tan^(-1)|((120)/(119)-(1)/(70))/(1+((120)/(119)xx(1)/(70)))|`
`=tan^(-1)|((8400-119)/(8330))/(1+(120)/(8330))|`
`=tan^(-1)|((8281)/(cancel(8330)))/((8450)/(cancel(8330)))|="tan"^(-1)(8281)/(8450)`
`therefore` Option (c) is correct.
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Conisder x = 4 tan^(-1)((1)/(5)),y = tan^(-1)((1)/(70))and z = tan^(-1)((1)/(99)) . What is x - y + z equal to ?

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