Question

Number of values of x satisfying the system of equations `sin^-1sqrt(2 + e^(-2x) - 2e^-x) + sec^-1sqrt(1 - x^2 + x^4) = π/2` and `5^(1+tan^-1x)` = 4 + [cos^–1x] is ______ (where [.] denotes greatest integer function)

विकल्प

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

Number of values of x satisfying the system of equations `sin^-1sqrt(2 + e^(-2x) - 2e^-x) + sec^-1sqrt(1 - x^2 + x^4) = π/2` and `5^(1+tan^-1x)` = 4 + [cos^–1x] is 1.00 (where [.] denotes greatest integer function)

Explanation:

∴ `sin^-1sqrt(1 + (e^-x + 1)^2) + sec^-1sqrt(1 - x^2(1 - x^2)) = π/2`  ...(1)

Equation (1) is only defined at x = 0 and x = 0 also satisfies the equation

`5^(1+tan^-1x)` = 4 + [cos^–1x]