Class 10 Exam > Class 10 Questions > SecA+tanA=1.5 then find the value of sinA?
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SecA+tanA=1.5 then find the value of sinA?
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SecA+tanA=1.5 then find the value of sinA?
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SecA+tanA=1.5 then find the value of sinA?
Solution:
Given:
SecA tanA=1.5
To find:
The value of sinA
Solution Steps:
Recall the trigonometric identities:
- SecA = 1/CosA
- TanA = SinA/CosA
Substituting the above identities in SecA TanA = 1.5, we get:
- 1/CosA * SinA/CosA = 1.5
- SinA/Cos²A = 1.5
- SinA = 1.5 Cos²A
Recall the trigonometric identity:
- Sin²A + Cos²A = 1
- Sin²A = 1 - Cos²A
Substituting the value of SinA in the above identity, we get:
- (1.5 Cos²A)² + Cos²A = 1
- 2.25 Cos⁴A + Cos²A - 1 = 0
Let's substitute Cos²A as x:
- 2.25x² + x - 1 = 0
Using the quadratic formula, we get:
- x = (-b ± √(b² - 4ac))/2a
- x = (-1 ± √(1 + 9))/4.5
- x = (-1 ± √10)/4.5
As Cos²A cannot be negative, we take the positive root:
- Cos²A = (-1 + √10)/4.5
Substituting this value in SinA = 1.5 Cos²A, we get:
- SinA = 1.5 * (-1 + √10)/4.5
- SinA = (-1 + √10)/9
Answer:
The value of sinA is (-1 + √10)/9.
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SecA+tanA=1.5 then find the value of sinA?
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SecA+tanA=1.5 then find the value of sinA? 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 SecA+tanA=1.5 then find the value of sinA? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for SecA+tanA=1.5 then find the value of sinA?.
SecA+tanA=1.5 then find the value of sinA? 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 SecA+tanA=1.5 then find the value of sinA? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for SecA+tanA=1.5 then find the value of sinA?.
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