Number of solutions of the equation cot−1(x2−12x)+tan−1(2xx2−1)=2π3 are
A
4
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B
1
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C
0
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D
None of these
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Solution
The correct option is A4 Case I: x2−12x>0 ⇒xϵ(−1,0)∪(1,∞) Given ⇒2tan−1(2xx2−1)=2π3 2xx2−1=√3⇒x=−1√3,√3 Case II: x2−12x<0 ⇒xϵ(−∞,−1)∪(0,1) Given ⇒π+2tan−1(2xx2−1)=−1√3⇒x=±2−√3 ∴ four solutions