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Express the trigonometric ratios tanA,secA in terms of cosecA?
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Express the trigonometric ratios tanA,secA in terms of cosecA?
Understanding Trigonometric Ratios
To express the trigonometric ratios tanA and secA in terms of cosecA, we begin by recalling some fundamental relationships between trigonometric functions.
Basic Definitions
- Cosecant (cosecA) is defined as:
- cosecA = 1/sinA
- The tangent (tanA) and secant (secA) functions are defined as:
- tanA = sinA/cosA
- secA = 1/cosA
Expressing tanA in Terms of cosecA
1. Start with the definition of cosecA:
- cosecA = 1/sinA
2. Rearranging gives:
- sinA = 1/cosecA
3. Now, substitute sinA into the tanA equation:
- tanA = sinA/cosA = (1/cosecA)/cosA
4. To find cosA in terms of cosecA, use the Pythagorean identity:
- cos^2A = 1 - sin^2A
- Substitute sinA using cosecA:
- cos^2A = 1 - (1/cosecA)^2
- This simplifies to:
- cosA = √(1 - 1/cosecA^2)
5. Thus, we have:
- tanA = (1/cosecA) / √(1 - 1/cosecA^2)
Expressing secA in Terms of cosecA
1. Start with secA:
- secA = 1/cosA
2. Using the same cosine relationship derived above:
- secA = 1/√(1 - 1/cosecA^2)
Final Expressions
- tanA = (1/cosecA) / √(1 - 1/cosecA^2)
- secA = 1/√(1 - 1/cosecA^2)
These relationships help in solving various trigonometric problems and demonstrate the interconnectedness of trigonometric functions.
To express the trigonometric ratios tanA and secA in terms of cosecA, we begin by recalling some fundamental relationships between trigonometric functions.
Basic Definitions
- Cosecant (cosecA) is defined as:
- cosecA = 1/sinA
- The tangent (tanA) and secant (secA) functions are defined as:
- tanA = sinA/cosA
- secA = 1/cosA
Expressing tanA in Terms of cosecA
1. Start with the definition of cosecA:
- cosecA = 1/sinA
2. Rearranging gives:
- sinA = 1/cosecA
3. Now, substitute sinA into the tanA equation:
- tanA = sinA/cosA = (1/cosecA)/cosA
4. To find cosA in terms of cosecA, use the Pythagorean identity:
- cos^2A = 1 - sin^2A
- Substitute sinA using cosecA:
- cos^2A = 1 - (1/cosecA)^2
- This simplifies to:
- cosA = √(1 - 1/cosecA^2)
5. Thus, we have:
- tanA = (1/cosecA) / √(1 - 1/cosecA^2)
Expressing secA in Terms of cosecA
1. Start with secA:
- secA = 1/cosA
2. Using the same cosine relationship derived above:
- secA = 1/√(1 - 1/cosecA^2)
Final Expressions
- tanA = (1/cosecA) / √(1 - 1/cosecA^2)
- secA = 1/√(1 - 1/cosecA^2)
These relationships help in solving various trigonometric problems and demonstrate the interconnectedness of trigonometric functions.
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Express the trigonometric ratios tanA,secA in terms of cosecA? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Express the trigonometric ratios tanA,secA in terms of cosecA? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Express the trigonometric ratios tanA,secA in terms of cosecA?.
Express the trigonometric ratios tanA,secA in terms of cosecA? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Express the trigonometric ratios tanA,secA in terms of cosecA? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Express the trigonometric ratios tanA,secA in terms of cosecA?.
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