Solve the equation- tan-1x-2-1x-2-3-

tan ^ 1x+2 ^ 1x=2π/3 tan ^ 1x+ ^ 1+ ^ 1x=2π/3 π/2+ ^ 1x=2π/3 ^ 1x=2π/3 π/2 ^ 1x=π/6 x=π/6 x=√(3) . ...

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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

Solve the equ...

Question

Solve the equation: ${tan}^{- 1} x + 2 {cot}^{- 1} x = \frac{2 π}{3}$ .

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Solution

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x

{tan}^{- 1} x + 2 {cot}^{- 1} x = \frac{2 π}{3}

x

{tan}^{- 1} x = \frac{1}{2} {cot}^{- 1} x

x

{tan}^{- 1} x + 2 {cot}^{- 1} x = \frac{2 π}{3}

{tan}^{- 1} x + 2 {cot}^{- 1} x = \frac{2 π}{3}

(\frac{1 - x}{1 + x}) - \frac{1}{2}

\frac{π}{12}

(\frac{8}{79})

\tan^{- 1} \frac{x}{2} + \tan^{- 1} \frac{x}{3} = \frac{π}{4}, 0 < x < \sqrt{6}

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