Question

Solve tan-12x + tan- 3x = -. (CBSE 2008, 09, 120, 13C]

11th - 12th Class

Maths

Solution

133

4.0 (1 ratings)

( tan ^{-1} 2 x+tan ^{-1} 3 x=frac{pi}{4} ) ( Rightarrow tan ^{-1}left(frac{2 x+3 x}{1-6 x^{2}}right)=frac{pi}{4} Rightarrow tan ^{-1}left(frac{5 x}{1-6 x^{2}}right)=frac{pi}{4} ) ( Rightarrow frac{5 x}{left(1-6 x^{2}right)}=tan frac{pi}{4}=1 Rightarrow 1-6 x^{2}=5 x ) ( Rightarrow 6 x^{2}+5 x-1=0 Rightarrow 6 x^{2}+6 x-x-1=0 ) ( Rightarrow 6 x(x+1)-(x+1)=0 Rightarrow(x+1)(6 x-1)=0 ) ( Rightarrow x=-1 quad ) or ( quad x=frac{1}{6} ) ( Rightarrow x=frac{1}{6} ) ( [because x=-1 mathrm{makes} text { LHS negative }] )