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Question

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 xy x+y

Simplify the given expression,

tan 1 ( x y ) tan 1 xy x+y = tan 1 ( x y xy x+y 1+( xy x+y )( x y ) ) = tan 1 ( ( x+y )xy( xy ) y( x+y ) y( x+y )+x( xy ) y( x+y ) ) = tan 1 ( x 2 +xyxy+ 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 xy x+y = tan 1 1 = π 4

Therefore, option © is correct.


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