tan-11-1-tan-11-yx + y17.is equal to(A)

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Solution

The given trigonometric expression is,

tan −1 ( x y )− tan −1 x−y x+y

Simplify the given expression,

tan −1 ( x y )− tan −1 x−y x+y = tan −1 ( x y − x−y x+y 1+( x−y x+y )( x y ) ) = tan −1 ( ( x+y )x−y( x−y ) y( x+y ) y( x+y )+x( x−y ) 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 )

Simplify further,

tan −1 ( x y )− tan −1 x−y x+y = tan −1 1 = π 4

Therefore, option © is correct.

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