Prove that tan^(-1)((1)/(2))+tan^(-1)((1...

Prove that `tan^(-1)((1)/(2))+tan^(-1)((1)/(5))+tan^(-1)((1)/(8))=(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:

`(pi)/(4) = R.H.S.`

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Show that tan ^(-1) ((1)/(2)) + tan ^( -1) ((1)/(5)) + tan^(-1) ""(1)/(8) = (pi)/(4).

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Knowledge Check

tan^(-1)(3/2)-tan^(-1)(1/5)=

A

`-(pi)/4`

B

`(pi)/2`

C

`(pi)/4`

D

`(3pi)/4`

4tan^(-1)(1/5)-tan^(-1)(1/239)=

A

`pi`

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`pi//2`

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`pi//4`

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`3pi//4`

2tan^(-1)(1)/(5)+sec^(-1)(5sqrt(2))/(7)+2tan^(-1)(1)/(8)=

A

`(pi)/(6)`

B

`(pi)/(4)`

C

`(pi)/(3)`

D

`(pi)/(8)`

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Prove that sin^(-1)((4)/(5))+2 Tan^(-1)((1)/(3)) = (pi)/2 .

Prove that: tan^(-1) ""(1)/(7) + tan^(-1) ""(1)/(13) - tan^(-1) ""(2)/(9) =0

Prove that (iii) 4 tan^(-1)"" (1)/(5) + tan^(-1)"" (1)/(99) - tan^(-1) "" (1)/( 70) = (pi)/(4)

Prove that (iii) tan^(-1) "" (3)/(4) + tan^(-1) "" (3)/(5) - tan^(-1)"" (8)/(19) = (pi)/(4)

5/3gt0,1/4gt0impliestan^(-1)(5/3)-tan^(-1)(1//4) =tan^(-1)((5/3-1/4)/(1+5/3. 1/4))=tan^(-1)(1)=(pi)/4

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