Find the value of tan(45°) + cot(45°).

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Question: Find the value of tan(45°) + cot(45°).

Options:

Correct Answer: 2

Solution:

tan(45°) = 1 and cot(45°) = 1, so 1 + 1 = 2.

Find the value of tan(45°) + cot(45°).

Find the value of tan(45°) + cot(45°).

Step 1: Understand what tan(45°) means. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
Step 2: Know that tan(45°) is equal to 1. This is because in a 45°-45°-90° triangle, the opposite and adjacent sides are equal.
Step 3: Understand what cot(45°) means. The cotangent is the reciprocal of the tangent, which means cot(θ) = 1/tan(θ).
Step 4: Since tan(45°) = 1, then cot(45°) = 1/tan(45°) = 1/1 = 1.
Step 5: Now add the two values together: tan(45°) + cot(45°) = 1 + 1.
Step 6: Calculate the sum: 1 + 1 = 2.

Trigonometric Functions – Understanding the values of basic trigonometric functions such as tangent and cotangent at specific angles.
Angle Relationships – Recognizing that tan(θ) and cot(θ) are reciprocal functions and their values at 45°.