Evaluate the expression: tan^(-1)(1) + tan^(-1)(1) + tan^(-1)(0).

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Question: Evaluate the expression: tan^(-1)(1) + tan^(-1)(1) + tan^(-1)(0).

Options:

Correct Answer: π/2

Solution:

tan^(-1)(1) = π/4, so the expression becomes π/4 + π/4 + 0 = π/2.

Evaluate the expression: tan^(-1)(1) + tan^(-1)(1) + tan^(-1)(0).

Evaluate the expression: tan^(-1)(1) + tan^(-1)(1) + tan^(-1)(0).

Step 1: Understand the notation tan^(-1)(x). This represents the inverse tangent function, also known as arctan. It gives the angle whose tangent is x.
Step 2: Calculate tan^(-1)(1). The angle whose tangent is 1 is π/4 (or 45 degrees).
Step 3: Calculate tan^(-1)(0). The angle whose tangent is 0 is 0 (or 0 degrees).
Step 4: Substitute the values into the expression: tan^(-1)(1) + tan^(-1)(1) + tan^(-1)(0) becomes π/4 + π/4 + 0.
Step 5: Add the values together: π/4 + π/4 = 2(π/4) = π/2.
Step 6: The final result of the expression is π/2.

Inverse Trigonometric Functions – Understanding the values of inverse tangent functions, particularly tan^(-1)(1) and tan^(-1)(0).
Addition of Angles – Applying the properties of addition for angles in trigonometric functions.