Evaluate the exact numerical value of: sin² 45° + cos² 60°.
Answer and explanation
Correct answer: D. 3/4
- Step 1: Exact values: sin 45° = 1/√2, so sin² 45° = (1/√2)² = 1/2. Step 2. cos 60° = 1/2, so cos² 60° = (1/2)² = 1/4. Step 3. Add values: 1/2 + 1/4 = 2/4 + 1/4 = 3/4. Answer: 3/4. Why not the others: 1/2 is sin² 45° alone; 1 assumes sin² θ + cos² θ for same angle; 5/4 is an arithmetic error.
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