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If ${(T a n^{- 1} x)}^{2} + {(C o t^{- 1} x)}^{2} = \frac{5 π^{2}}{8}$ then $x =$

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Correct option is A

Tan-1x2+Cot-1x2=5π28 ⇒Tan-1x+Cot-1x2-2Tan-1xCot-1x=5π28⇒Tan-1x+Cot-1x2-2Tan-1xπ2-Tan-1x=5π28⇒2Tan-1x2-πTan-1x-3π28=0⇒Tan-1x=π4,3π4But Tan-1x=π4 cannot satisfy the equation. ⇒Tan-1x=3π4⇒x=-1

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IfTan−1x2+Cot−1x2=5π28thenx=

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Ready to Test Your Skills?

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If ${(T a n^{- 1} x)}^{2} + {(C o t^{- 1} x)}^{2} = \frac{5 π^{2}}{8}$ then $x =$