Trigonometric Identities
Easymathematics
The identity 1 + tan²θ equals
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Solution
Incorrect! Answer:
sec²θ
- Start with Basic Identity: sin2θ+cos2θ=1.
- Transformation: Divide the entire equation by cos2θ.
- Divide Term-wise:
- cos2θsin2θ+cos2θcos2θ=cos2θ1.
- Apply Definitions:
- tan2θ+1=sec2θ.
- Domain Note: This identity holds for all θ where cosθ=0.
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About This Question
- Subject
- mathematics
- Chapter
- trigonometry
- Topic
- trigonometric identities
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
sec²θ
- Start with Basic Identity: sin2θ+cos2θ=1.
- Transformation: Divide the entire equation by cos2θ.
- Divide Term-wise:
- cos2θsin2θ+cos2θcos2θ=cos2θ1.
- Apply Definitions:
- tan2θ+1=sec2θ.
- Domain Note: This identity holds for all θ where cosθ=0.
This easy difficulty mathematics question is from the chapter trigonometry, covering the topic of trigonometric identities. It appeared in the 2025 exam.
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