Class 10 Exam > Class 10 Questions > If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA...
Start Learning for Free
If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2?
Verified Answer
If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove...
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
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,
- \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 2 \)
- \( (x^2/a^2 + y^2/b^2) = 2 \)
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2?
Question Description
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 2024 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 2024 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 2024 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 2024 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?.
Solutions for If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2? defined & explained in the simplest way possible. Besides giving the explanation of
If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2?, a detailed solution for If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2? has been provided alongside types of If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2? theory, EduRev gives you an
ample number of questions to practice If ( x/a sinA - y/b cosA ) = 1 and ( x/a cosA y/b sinA ) = 1 , prove that (x²/a² y²/b² ) = 2? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup