Trigonometry
Trigonometric Ratios, Standard Angles
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Grade None
Question:
If sin 45° × cos 45° = a and tan 45° × cot 45° = b, find a + b.
A. 1/2
B. 3/2
C. 5/2
D. 7/2
Step-by-Step Solution
Key Concept: Use standard trigonometric values.
Step 1: sin 45° × cos 45° = (1/√2)(1/√2) = 1/2. So a = 1/2. Step 2: tan 45° × cot 45° = 1 × 1 = 1. So b = 1. Step 3: a + b = 1/2 + 1 = 3/2.
Correct Answer: B
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