Evaluate tan-1xy-tan-1x-yx+y is
π2
π3
π4
π4or-3π4
Explanation for the correct option:
Find the value of the given Equation.
Consider the given Equation as,
tan-1xy-tan-1x-yx+y
Rewrite the above Equation by dividing the second term of the Equation by y as,
⇒tan-1xy-tan-1x-yyx+yy=tan-1xy-tan-1xy-11+xy=tan-1xy-tan-1xy-tan-11[∵tan-1A-tan-1B=tan-1(A-B1+A.B)]=tan-1xy-tan-1xy+tan-11=tan-11=π4[∵tan-11=π4]
Therefore,
tan-1xy-tan-1x-yx+y=π4
Hence, option (C) is the correct answer.