Question

If θ = `sin^-1((2x)/(1 + x^2)) + cos^-1((1 - x^2)/(1 + x^2))`, for `x ≥ 3/2` then the absolute value of `((cosθ + tanθ + 4)/secθ)` is ______.

Options

• 2.00

• 3.00

• 4.00

• 5.00

Answer 1

If θ = `sin^-1((2x)/(1 + x^2)) + cos^-1((1 - x^2)/(1 + x^2))`, for `x ≥ 3/2` then the absolute value of `((cosθ + tanθ + 4)/secθ)` is 3.00.

Explanation:

For `x ≥ 3/2`; θ = π

∴ `(cosπ + sinπ + 4)/secπ = (-1 + 4)/-1` = –3