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If secA+tanA=m then prove that secA=m²+1/2m?
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If secA+tanA=m then prove that secA=m²+1/2m?
Given Condition
Let secA + tanA = m.
We need to prove that secA = (m² + 1) / (2m).
Using Trigonometric Identities
- Recall the identity:
sec²A - tan²A = 1.
This can be rearranged as:
sec²A = tan²A + 1.
Expressing tanA in terms of m
- From the given m, we can express tanA:
tanA = m - secA.
Substituting tanA in the identity
- Substitute tanA into the identity:
sec²A = (m - secA)² + 1.
- Expanding the right side:
sec²A = (m² - 2m*secA + sec²A) + 1.
Rearranging the equation
- By simplifying the equation:
0 = m² - 2m*secA + 1.
- Rearranging gives:
2m*secA = m² + 1.
Final Step
- Now, divide both sides by 2m:
secA = (m² + 1) / (2m).
Conclusion
Thus, we have proved that if secA + tanA = m, then secA = (m² + 1) / (2m).
Let secA + tanA = m.
We need to prove that secA = (m² + 1) / (2m).
Using Trigonometric Identities
- Recall the identity:
sec²A - tan²A = 1.
This can be rearranged as:
sec²A = tan²A + 1.
Expressing tanA in terms of m
- From the given m, we can express tanA:
tanA = m - secA.
Substituting tanA in the identity
- Substitute tanA into the identity:
sec²A = (m - secA)² + 1.
- Expanding the right side:
sec²A = (m² - 2m*secA + sec²A) + 1.
Rearranging the equation
- By simplifying the equation:
0 = m² - 2m*secA + 1.
- Rearranging gives:
2m*secA = m² + 1.
Final Step
- Now, divide both sides by 2m:
secA = (m² + 1) / (2m).
Conclusion
Thus, we have proved that if secA + tanA = m, then secA = (m² + 1) / (2m).
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If secA+tanA=m then prove that secA=m²+1/2m?
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If secA+tanA=m then prove that secA=m²+1/2m? 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 If secA+tanA=m then prove that secA=m²+1/2m? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If secA+tanA=m then prove that secA=m²+1/2m?.
If secA+tanA=m then prove that secA=m²+1/2m? 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 If secA+tanA=m then prove that secA=m²+1/2m? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If secA+tanA=m then prove that secA=m²+1/2m?.
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