Question

18.The value of x satisfying the equation tan⁻¹(1/2+√3)-tan⁻¹(1/x)=tan⁻¹(1/3) is 
(a) x = 2
b)x=1/2
c)x=1/2-√3
d) none​

Answer 1

Step-by-step explanation:

given,

tan^-1(1/2+√3)-tan^-1(1/x)=tan^-1(1/3)

tan^-1[1/2+√3-1/x/1+(1/2+√3)(1/x)]=tan^-1(1/3)

tan^-1[(x+2√3x-1 )(2x)/(2x)(2x+1+2√3)]= tan^-1(1/3)

tan^-1[x+2√3x-1/2x+1+2√3]= tan^-1(1/3)

x+2√3x-1/2x+1+2√3=1/3

x=1+3+2√3-6√3

x=4(1-√3)

therefore the required value of x is 4(1-√3)