Question

of equations: (b) tan- + tan- - 1 + 4x =tan-1- 1 + 2 x lanı 2

JEE/Engineering Exams

Maths

Solution

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( tan ^{-1}left(frac{1}{1+2 x}right)+tan ^{-1}left(frac{1}{4 x}right)=tan ^{-1} frac{2}{x^{2}} ) ( Rightarrow tan ^{-1}left(frac{frac{1}{1+2 x}+frac{1}{1+4 x}}{1-frac{1}{1+2 x} cdot frac{1}{1+4 x}}right)=tan ^{-1} frac{2}{x^{2}} ) A tan ( ^{-1}left(frac{1+4 x+1+2 x}{1+2 x)(1+4 x)-1}right)=tan ^{-1}left(frac{2}{x^{2}}right) ) ( Rightarrow tan ^{-1}left(frac{6 x+2}{1+6 x+8 x^{2}+1}right)=tan ^{-1}left(frac{2}{x^{2}}right) ) if ( frac{6 x+2}{6 x+8 x^{2}}=frac{2}{x^{2}} ) 7 ( x^{2}(3 x+1)=2left(3 x+9 x^{2}right) ) ( 3 x^{3}+x^{2}-6 x-8 x^{2}=0 ) ( 3 x^{2}-6 x=0 ) ( 3 x^{3}-8 x-7 x^{2}-6 ) 2) ( theta ) ( xleft(3 x^{2}-7 x-6right)=0 ) ( xleft(3 x^{2}-9 x+2 x-6right)=0 ) ( x(3 x(8 x-3)+2(x-3))=0 ) ( x(3 x+2)(x-3)=0 quad ) a ( frac{61+0}{x=3} )