If x = tan^(-1)(1), then the value of x is:

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Question: If x = tan^(-1)(1), then the value of x is:

Options:

Correct Answer: π/4

Solution:

tan^(-1)(1) = π/4.

If x = tan^(-1)(1), then the value of x is:

If x = tan^(-1)(1), then the value of x is:

Step 1: Understand that tan^(-1)(1) means we are looking for an angle whose tangent is 1.
Step 2: Recall that the tangent of an angle is equal to the opposite side divided by the adjacent side in a right triangle.
Step 3: The angle where the tangent is 1 occurs when both the opposite and adjacent sides are equal.
Step 4: The angle that satisfies this condition is 45 degrees, which is equivalent to π/4 radians.
Step 5: Therefore, if x = tan^(-1)(1), then x = π/4.

Inverse Trigonometric Functions – Understanding the values of inverse trigonometric functions, specifically the arctangent function.
Special Angles – Knowledge of special angles in trigonometry, particularly that tan(π/4) = 1.