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The function f(x) = tan⁻¹(sin x + cos x) is an increasing function in

1. (0, π/2)
2. (-π/2, π/2)
3. (-π/4, π/4)
4. (-π/2, π/4)

Correct answer: (-π/2, π/4)

Solution

The function f(x) = tan⁻¹(sin x + cos x) is increasing in the interval (-π/2, π/4) because the derivative of the function is positive in this range, indicating that the function's output increases as x increases.

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