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If k+1 = sec^theta(1+ sin theta) (1-sin theta) , then find the value of k?
Most Upvoted Answer
If k+1 = sec^theta(1+ sin theta) (1-sin theta) , then find the value o...
Solution:
Given:
k1 = sec^θ(1 - sinθ)(1 - sinθ)
To Find:
Value of k
Approach:
We know that secθ = 1/cosθ
Therefore, k1 can be written as:
k1 = (1/cosθ)(1 - sinθ)(1 - sinθ)
k1 = (1 - sinθ)(1 - sinθ)/cosθ
k1 = (cos²θ)/cosθ - 2sinθ(cosθ)/cosθ + sin²θ
k1 = cosθ - 2sinθ + sin²θ/cosθ
Let's simplify the expression:
k1 = 1/cosθ - 2sinθ/cosθ + sin²θ/cosθ
k1 = secθ - 2tanθ + tan²θ
As we know that secθ = 1/cosθ and tanθ = sinθ/cosθ, the expression can be written as:
k1 = secθ - 2sinθ/cosθ + (sinθ/cosθ)²
k1 = secθ - 2sinθ/cosθ + sin²θ/cos²θ
k1 = secθ - 2sinθ/cosθ + (1 - cos²θ)/cos²θ
k1 = secθ - 2sinθ/cosθ + 1/cos²θ - 1
k1 = (secθ + tanθ)² - 1
Therefore, the value of k is:
k = (secθ + tanθ)² - 1 - k1
Answer:
The value of k is (secθ + tanθ)² - 1 - k1.
Community Answer
If k+1 = sec^theta(1+ sin theta) (1-sin theta) , then find the value o...
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If k+1 = sec^theta(1+ sin theta) (1-sin theta) , then find the value of k?
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If k+1 = sec^theta(1+ sin theta) (1-sin theta) , then find the value of k? 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 k+1 = sec^theta(1+ sin theta) (1-sin theta) , then find the value of k? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If k+1 = sec^theta(1+ sin theta) (1-sin theta) , then find the value of k?.
If k+1 = sec^theta(1+ sin theta) (1-sin theta) , then find the value of k? 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 k+1 = sec^theta(1+ sin theta) (1-sin theta) , then find the value of k? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If k+1 = sec^theta(1+ sin theta) (1-sin theta) , then find the value of k?.
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