Which of the following is true? sin² 60⁰ + cos² 60⁰ = 1, sin² 45⁰ + cos² 45⁰ = 1, sin² 45⁰ − cos² 45⁰ = 0, All of these
- sin² 60⁰ + cos² 60⁰ = 1
- sin² 45⁰ + cos² 45⁰ = 1
- sin² 45⁰ − cos² 45⁰ = 0
- All of these
Explanation
Let's evaluate each option:
1. sin² 60⁰ + cos² 60⁰ = 1
sin 60⁰ = √3/2, cos 60⁰ = 1/2
(√3/2)² + (1/2)² = 3/4 + 1/4 = 1
2. sin² 45⁰ + cos² 45⁰ = 1
sin 45⁰ = cos 45⁰ = 1/√2
(1/√2)² + (1/√2)² = 1/2 + 1/2 = 1
3. sin² 45⁰ − cos² 45⁰ = 0
(1/√2)² - (1/√2)² = 1/2 - 1/2 = 0
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