cos inverse ( x^2 - 1 / x^2 + 1 ) + tan inverse ( 2x / x^2 - 1 - Maths - Inverse Trigonometric Functions

Question

cos inverse ( x^2 - 1 / x^2 + 1 ) + tan inverse ( 2x / x^2 - 1 ) =
2 pie / 3

Garima Singhal · Accepted Answer

cos-1x2-1x2+1+tan-12xx2-1=2π3⇒cos-1-1-x21+x2 + tan-1-2x1-x2 = 2π3⇒π-cos-11-x21+x2-tan-12x1-x2=2π3put x = tan θπ-cos-11-tan2θ1+tan2θ-tan-12 tan θ1-tan2θ=2π3⇒cos-1cos 2θ + tan-1tan 2θ = π3⇒2θ + 2θ = π3⇒2tan-1x + 2tan-1x=π3⇒tan-1x=π12⇒x=tanπ12

cos inverse ( x^2 - 1 / x^2 + 1 ) + tan inverse ( 2x / x^2 - 1 ) = 2 pie / 3