Question

maximum value of sec inverse X square + Cosec inverse x square

Answer 1

Given :

A trigonometric equation

sec^-¹ x² + cosec^-¹ x²

To Find :

Maximum value of given trigonometric equation i.e. maximum value of x sec^-¹ x² + cosec^-¹ x²

Solution :

•Given equation is sec^-¹ x² + cosec^-¹ x²

let it's value be y

so, y = sec^-¹ x² + cosec^-¹ x²

•Also, sec^-¹ x + cosec^-¹ x = π/2

for all x belongs to

(-infinity , -1)U(1 , infinity)

•Hence , value of

sec^-¹ x² + cosec^-¹ x² is π/2 which is constant .

•So, maximum value of given trigonometric equation i.e.

sec^-¹ x² + cosec^-¹ x² is π/2