The sum of possible values of x for tan-1(x+1)+cot-11(x-1)=tan-1831 is
–334
–324
–314
–304
Explanation for the correct option:
Find the required sum.
Given:tan-1(x+1)+cot-11(x-1)=tan-1831
⇒tan-1(x+1)+tan-1(x-1)=tan-1831∵cot-11x-1=tan-1(x-1)⇒tan-1x+1+x-11-(x+1)(x-1)=tan-1831∵tan-1A+tan-1B=tan-1A+B1-AB⇒2x1-x2-12=831⇒2x2-x2=831⇒62x=16-8x2⇒8x2+62x-16=0⇒4x2+31x-8=0⇒4x2+32x-x-8=0⇒4xx+8-1(x+8)=0⇒4x-1x+8=0⇒x=14orx=-8
So, the sum of possible values of x is 14+–8=-314
Hence, option (C) is the correct answer.