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A^2 b^2a^2 b^2-c^2/c^2 a^2-b^2=tanA/tanB?
Most Upvoted Answer
A^2 b^2a^2 b^2-c^2/c^2 a^2-b^2=tanA/tanB?
Solution:
Step 1: Simplifying the left-hand side
We start by simplifying the left-hand side of the equation:
A²B²A²B² - C² / C²A² - B²
Expanding A²B²A²B², we get:
(AxAxA)(BxBxB)(AxAxA)(BxBxB) - C² / C²A² - B²
Which simplifies to:
A^6B^6 - C^2 / C^2(A^2 - B^2)
Using the identity A² - B² = (A + B)(A - B), we can simplify further:
A^6B^6 - C^2 / C²(A + B)(A - B)
Now we can simplify the expression by factoring out A²B²:
A²B²(A²B² - C²) / C²(A + B)(A - B)
Step 2: Simplifying the right-hand side
Now we simplify the right-hand side of the equation:
tanA / tanB
Using the identity tanA = sinA / cosA and tanB = sinB / cosB, we get:
sinAcosB / cosAsinB
Which simplifies to:
sinA / sinB * cosB / cosA
Using the identity sin²θ + cos²θ = 1, we can rewrite this as:
(sinA / sinB) * √(1 - sin²B) / √(1 - sin²A)
Step 3: Equating the left-hand side and right-hand side
Now we equate the left-hand side and right-hand side of the equation:
A²B²(A²B² - C²) / C²(A + B)(A - B) = (sinA / sinB) * √(1 - sin²B) / √(1 - sin²A)
Using the identity sin²θ + cos²θ = 1, we can simplify the expression:
A²B²(A²B² - C²) / C²(A + B)(A - B) = (sinA / sinB) * cosB / cosA
Now we can simplify further by cross-multiplying and canceling out common factors:
A²B²(A²B² - C²)cosB = C²(sinA)(A + B)(A - B)cosA
Dividing both sides by A²B²(A²B² - C²)cosAcosB, we get:
(sinA / sinB) = C / √(A²B² - C²)
Now we can use the identity A
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A^2 b^2a^2 b^2-c^2/c^2 a^2-b^2=tanA/tanB?
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A^2 b^2a^2 b^2-c^2/c^2 a^2-b^2=tanA/tanB? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A^2 b^2a^2 b^2-c^2/c^2 a^2-b^2=tanA/tanB? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A^2 b^2a^2 b^2-c^2/c^2 a^2-b^2=tanA/tanB?.
A^2 b^2a^2 b^2-c^2/c^2 a^2-b^2=tanA/tanB? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A^2 b^2a^2 b^2-c^2/c^2 a^2-b^2=tanA/tanB? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A^2 b^2a^2 b^2-c^2/c^2 a^2-b^2=tanA/tanB?.
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