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Let (tan α) x + (sin α) y = α and (α cosec α) x + (cos α) y = 1 be two variable straight lines, α being the
parameter. Let P be the point of intersection of the lines. In the limiting position when α→ 0, the
coordinates of P are
parameter. Let P be the point of intersection of the lines. In the limiting position when α→ 0, the
coordinates of P are
- a)(2 , 1)
- b)(2 , –1)
- c)(–2 , 1)
- d)(–2 ,–1)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let (tan α) x + (sin α) y = αand (αcosec &alph...
Solving tanα.x + sinα.y = α and α cosecα.x + cosα.y = 1, we get
x = (αcosα−sinα)/(sinα−α)
and y = (α−xtanα)/sinα
lim x(α→0) = lim(α→0) (cosα − αsinα − cosα)/(cosα−1)
= lim (α→0) αsinα/(2sin2(α/2))
= lim (α→0) [4(α/2)2(sinα/α)]/[(sinα/2)2]/2 = 2
lim y(α→0) = lim(α→α) (α−xtanα)/(sinα)
= lim(α→0) (α/sinα − x/cosα)
= 1 − 2
= − 1
Hence P = (2,−1)
x = (αcosα−sinα)/(sinα−α)
and y = (α−xtanα)/sinα
lim x(α→0) = lim(α→0) (cosα − αsinα − cosα)/(cosα−1)
= lim (α→0) αsinα/(2sin2(α/2))
= lim (α→0) [4(α/2)2(sinα/α)]/[(sinα/2)2]/2 = 2
lim y(α→0) = lim(α→α) (α−xtanα)/(sinα)
= lim(α→0) (α/sinα − x/cosα)
= 1 − 2
= − 1
Hence P = (2,−1)
Most Upvoted Answer
Let (tan α) x + (sin α) y = αand (αcosec &alph...
Let \( \tan(\theta) = x \).
Using the identity \( \tan^2(\theta) + 1 = \sec^2(\theta) \), we can rewrite the equation as:
\( \tan^2(\theta) + \tan(\theta) - 1 = 0 \).
Substituting \( x \) for \( \tan(\theta) \), we get:
\( x^2 + x - 1 = 0 \).
Using the quadratic formula, we can solve for \( x \):
\( x = \frac{-1 \pm \sqrt{1^2 - 4(1)(-1)}}{2(1)} = \frac{-1 \pm \sqrt{5}}{2} \).
Therefore, \( \tan(\theta) = \frac{-1 \pm \sqrt{5}}{2} \).
Using the identity \( \tan^2(\theta) + 1 = \sec^2(\theta) \), we can rewrite the equation as:
\( \tan^2(\theta) + \tan(\theta) - 1 = 0 \).
Substituting \( x \) for \( \tan(\theta) \), we get:
\( x^2 + x - 1 = 0 \).
Using the quadratic formula, we can solve for \( x \):
\( x = \frac{-1 \pm \sqrt{1^2 - 4(1)(-1)}}{2(1)} = \frac{-1 \pm \sqrt{5}}{2} \).
Therefore, \( \tan(\theta) = \frac{-1 \pm \sqrt{5}}{2} \).
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Let (tan α) x + (sin α) y = αand (αcosec &alph...
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Let (tan α) x + (sin α) y = αand (αcosec α) x + (cos α) y = 1 be two variable straight lines, αbeing theparameter. Let P be the point of intersection of the lines. In the limiting position when α→0, thecoordinates of P area)(2 , 1)b)(2 , –1)c)(–2 , 1)d)(–2 ,–1)Correct answer is option 'B'. Can you explain this answer?
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Let (tan α) x + (sin α) y = αand (αcosec α) x + (cos α) y = 1 be two variable straight lines, αbeing theparameter. Let P be the point of intersection of the lines. In the limiting position when α→0, thecoordinates of P area)(2 , 1)b)(2 , –1)c)(–2 , 1)d)(–2 ,–1)Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let (tan α) x + (sin α) y = αand (αcosec α) x + (cos α) y = 1 be two variable straight lines, αbeing theparameter. Let P be the point of intersection of the lines. In the limiting position when α→0, thecoordinates of P area)(2 , 1)b)(2 , –1)c)(–2 , 1)d)(–2 ,–1)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let (tan α) x + (sin α) y = αand (αcosec α) x + (cos α) y = 1 be two variable straight lines, αbeing theparameter. Let P be the point of intersection of the lines. In the limiting position when α→0, thecoordinates of P area)(2 , 1)b)(2 , –1)c)(–2 , 1)d)(–2 ,–1)Correct answer is option 'B'. Can you explain this answer?.
Let (tan α) x + (sin α) y = αand (αcosec α) x + (cos α) y = 1 be two variable straight lines, αbeing theparameter. Let P be the point of intersection of the lines. In the limiting position when α→0, thecoordinates of P area)(2 , 1)b)(2 , –1)c)(–2 , 1)d)(–2 ,–1)Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let (tan α) x + (sin α) y = αand (αcosec α) x + (cos α) y = 1 be two variable straight lines, αbeing theparameter. Let P be the point of intersection of the lines. In the limiting position when α→0, thecoordinates of P area)(2 , 1)b)(2 , –1)c)(–2 , 1)d)(–2 ,–1)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let (tan α) x + (sin α) y = αand (αcosec α) x + (cos α) y = 1 be two variable straight lines, αbeing theparameter. Let P be the point of intersection of the lines. In the limiting position when α→0, thecoordinates of P area)(2 , 1)b)(2 , –1)c)(–2 , 1)d)(–2 ,–1)Correct answer is option 'B'. Can you explain this answer?.
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Let (tan α) x + (sin α) y = αand (αcosec α) x + (cos α) y = 1 be two variable straight lines, αbeing theparameter. Let P be the point of intersection of the lines. In the limiting position when α→0, thecoordinates of P area)(2 , 1)b)(2 , –1)c)(–2 , 1)d)(–2 ,–1)Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Let (tan α) x + (sin α) y = αand (αcosec α) x + (cos α) y = 1 be two variable straight lines, αbeing theparameter. Let P be the point of intersection of the lines. In the limiting position when α→0, thecoordinates of P area)(2 , 1)b)(2 , –1)c)(–2 , 1)d)(–2 ,–1)Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Let (tan α) x + (sin α) y = αand (αcosec α) x + (cos α) y = 1 be two variable straight lines, αbeing theparameter. Let P be the point of intersection of the lines. In the limiting position when α→0, thecoordinates of P area)(2 , 1)b)(2 , –1)c)(–2 , 1)d)(–2 ,–1)Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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