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If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2?
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If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove...
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If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove...
Let's start by squaring both sides of the given equations:
1. \((\frac{x}{a} \sin A - \frac{y}{b} \cos A)^2 = 1^2\)
2. \((\frac{x}{a} \cos A + \frac{y}{b} \sin A)^2 = 1^2\)
Expand and simplify these expressions. Then, add the two resulting equations together. The left side should simplify to \(\frac{x^2}{a^2} + \frac{y^2}{b^2}\). Simplify the right side, and you should arrive at \(2\).
1. \((\frac{x}{a} \sin A - \frac{y}{b} \cos A)^2 = 1^2\)
2. \((\frac{x}{a} \cos A + \frac{y}{b} \sin A)^2 = 1^2\)
Expand and simplify these expressions. Then, add the two resulting equations together. The left side should simplify to \(\frac{x^2}{a^2} + \frac{y^2}{b^2}\). Simplify the right side, and you should arrive at \(2\).
Community Answer
If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove...
Proof:
Given Equations:
- \( \frac{x}{a} \sin A - \frac{y}{b} \cos A = 1 \)
- \( \frac{x}{a} \cos A + \frac{y}{b} \sin A = 1 \)
Square both equations:
- \( (\frac{x}{a} \sin A - \frac{y}{b} \cos A)^2 = 1^2 \)
- \( (\frac{x}{a} \cos A + \frac{y}{b} \sin A)^2 = 1^2 \)
Expand and simplify:
- \( \frac{x^2}{a^2} \sin^2 A - 2 \frac{xy}{ab} \sin A \cos A + \frac{y^2}{b^2} \cos^2 A = 1 \)
- \( \frac{x^2}{a^2} \cos^2 A + 2 \frac{xy}{ab} \sin A \cos A + \frac{y^2}{b^2} \sin^2 A = 1 \)
Add the two equations:
- \( \frac{x^2}{a^2} (\sin^2 A + \cos^2 A) + \frac{y^2}{b^2} (\cos^2 A + \sin^2 A) = 2 \)
- \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 2 \)
Therefore,
- \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 2 \)
- \( (x^2/a^2 + y^2/b^2) = 2 \)
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If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2?.
If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2?.
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