Multiple Angles
Mediummathematics
The formula cos 2θ can be written as
Select the correct option:
Solution
Incorrect! Answer:
All of these
- Basic Double Angle: cos2θ=cos2θ−sin2θ.
- Transform using sin2θ=1−cos2θ:
- cos2θ=cos2θ−(1−cos2θ)=2cos2θ−1.
- Transform using cos2θ=1−sin2θ:
- cos2θ=(1−sin2θ)−sin2θ=1−2sin2θ.
- Result: All three expressions are mathematically identical and highly useful in calculus.
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About This Question
- Subject
- mathematics
- Chapter
- trigonometry
- Topic
- multiple angles
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
All of these
- Basic Double Angle: cos2θ=cos2θ−sin2θ.
- Transform using sin2θ=1−cos2θ:
- cos2θ=cos2θ−(1−cos2θ)=2cos2θ−1.
- Transform using cos2θ=1−sin2θ:
- cos2θ=(1−sin2θ)−sin2θ=1−2sin2θ.
- Result: All three expressions are mathematically identical and highly useful in calculus.
This medium difficulty mathematics question is from the chapter trigonometry, covering the topic of multiple angles. It appeared in the 2025 exam.
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