Number of solutions of the equation tan-1x 2 -cot-1x 2 -5-2-8 is

The given can be written as π^2/4 2 tan^ 1 x(π/2 tan^ 1x )=5π^2/8⇒ tan^ 1x= π/4, 3π/4 ...

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Properties Derived from Trigonometric Identities

Number of sol...

Question

Number of solutions of the equation ${(t a n^{- 1} x)}^{2} + {(c o t^{- 1} x)}^{2} = \frac{5 π^{2}}{8}$ is

Infinite

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{({tan}^{- 1} x)}^{2} + {({cot}^{- 1} x)}^{2} = \frac{5 π^{2}}{8}

{({t a n}^{- 1} x)}^{2} + {({c o t}^{- 1} x)}^{2} = \frac{{5 π}^{2}}{8}

${(t a n^{- 1} x)}^{2} + {(c o t^{- 1} x)}^{2} = \frac{5 π^{2}}{8} \Rightarrow x =$

(t a n^{- 1} x)^{2} + (c o t^{- 1} x)^{2} = \frac{5 π^{2}}{8}

x

(t a n^{- 1} x)^{2} + (c o t^{- 1} x)^{2} = 5 π^{2} / 8

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