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tan −1 x+cot −1x= π/2,x∈ R ​

\(\begin{array}{l}tan^{-1}x+cot^{-1}x=\frac{\pi }{2},x\epsilon \dot{R}\end{array} \) tan<sup>-1</sup>+cot<sup>-1</sup>x Let tan<sup>-1</sup>x=A tan A=x cor(π/2-A)=x cot<sup>-1</sup>x=π/2-A tan<sup>-1</sup>x+cot<sup>-1</sup>x A+π/2-A π/2

Solve: √2x+9+x=13

\(\begin{array}{l}\sqrt{2x+9}+x=13\end{array} \) \(\begin{array}{l}\sqrt{2x+9}=13-x\end{array} \) On squaring, we get 2x+9x<sup>2</sup>+169-26x x<sup>2</sup>+160-28x=0 x<sup>2</sup>-20x-8x+160=0 (x-20)(x-8)=0 Therefore, x=20 or x=8 However, x=20 does not... View Article