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Prove that tan^(-1)(x/y)- tan^(-1)((x-y)...

Prove that `tan^(-1)(x/y)- tan^(-1)((x-y)/(x+y)) ` is ` (pi)/4` and Not `(-3pi)/4` .

Text Solution

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`tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))`
`tan^(-1)((x/y)-((x-y)/(x+y)))/((x/y)*((x-y)/(x+y))`
`tan^(-1)((x^2+xy-xy+y^2)/(xy+y^2+x^2-xy))`
`tan^(-1)((x^2+y^2)/(x^2+y^2))`
`tan^(-1)(1)`
`pi/4`.
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tan^(-1)x+tan^(-1)y=pi+tan^(-1)((x+y)/(1-xy))

tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y)) is (A) pi/2 (B) pi/3 (C) pi/4 (D) pi/4 or (3pi)/4

tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y)) is (A) pi/2 (B) pi/3 (C) pi/4 (D) pi/4 or (3pi)/4

tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y)) is (A) pi/2 (B) pi/3 (C) pi/4 (D) pi/4 or (3pi)/4

tan^(-1)(x/y)-tan^(-1)(x-y)/(x+y) is equal to(A) pi/2 (B) pi/3 (C) pi/4 (D) (-3pi)/4

tan^(-1)(x/y)-tan^(-1)(x-y)/(x+y) is equal to (A) pi/2 (B) pi/3 (C) pi/4 (D) (-3pi)/4

tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y)) is equal to (A) pi/2 (B) pi/3 (C) pi/4 (D) (-3pi)/4

tan^(-1)((x)/(y))-tan^(-1)((x-y)/(x+y)) is (A) (pi)/(2)(B)(pi)/(3)(C)(pi)/(4)(D)(pi)/(4) or 3(pi)/(4) is (A) (pi)/(2)(B)

If tan ^(-1) x-tan ^(-1) y=-(pi)/(4) then