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If tan (cotx) = cot(tanx), then sin2x is equal to
- a)2/(2n+1)π
- b)4/(2n+1)π
- c)2/n(n+1)π
- d)4/n(n+1)π
Correct answer is option 'B'. Can you explain this answer?
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If tan (cotx) = cot(tanx), then sin2x is equal toa)2/(2n+1)πb)4/(2n...
Explanation:
- Given: tan(cotx) = cot(tanx)
- We know that tan(x) = 1/cot(x) and cot(x) = 1/tan(x)
- Therefore, tan(cotx) = 1/cot(cotx) and cot(tanx) = 1/tan(tanx)
Using the given equation:
- tan(cotx) = cot(tanx)
- 1/cot(cotx) = 1/tan(tanx)
- cot(cotx) = tan(tanx)
Using the trigonometric identity:
- cot(x) = 1/tan(x), so cot(cotx) = 1/tan(cotx)
- tan(x) = 1/cot(x), so tan(tanx) = 1/cot(tanx)
Substitute back into the equation:
- 1/tan(cotx) = 1/cot(tanx)
- tan(tanx) = cot(cotx)
- tan(tanx) = tan(cotx)
Equating the angles:
- tanx = cotx
- tanx = 1/tanx
- tan^2x = 1
- sin^2x/cos^2x = 1
- sin^2x = cos^2x
Using the trigonometric identity sin^2x + cos^2x = 1:
- sin^2x + sin^2x = 1
- 2sin^2x = 1
- sin^2x = 1/2
Therefore, sin^2x is equal to 1/2 which can be written as 2/(2n+1)π. Option B is the correct answer.
- Given: tan(cotx) = cot(tanx)
- We know that tan(x) = 1/cot(x) and cot(x) = 1/tan(x)
- Therefore, tan(cotx) = 1/cot(cotx) and cot(tanx) = 1/tan(tanx)
Using the given equation:
- tan(cotx) = cot(tanx)
- 1/cot(cotx) = 1/tan(tanx)
- cot(cotx) = tan(tanx)
Using the trigonometric identity:
- cot(x) = 1/tan(x), so cot(cotx) = 1/tan(cotx)
- tan(x) = 1/cot(x), so tan(tanx) = 1/cot(tanx)
Substitute back into the equation:
- 1/tan(cotx) = 1/cot(tanx)
- tan(tanx) = cot(cotx)
- tan(tanx) = tan(cotx)
Equating the angles:
- tanx = cotx
- tanx = 1/tanx
- tan^2x = 1
- sin^2x/cos^2x = 1
- sin^2x = cos^2x
Using the trigonometric identity sin^2x + cos^2x = 1:
- sin^2x + sin^2x = 1
- 2sin^2x = 1
- sin^2x = 1/2
Therefore, sin^2x is equal to 1/2 which can be written as 2/(2n+1)π. Option B is the correct answer.
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If tan (cotx) = cot(tanx), then sin2x is equal toa)2/(2n+1)πb)4/(2n+1)πc)2/n(n+1)πd)4/n(n+1)πCorrect answer is option 'B'. Can you explain this answer?
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If tan (cotx) = cot(tanx), then sin2x is equal toa)2/(2n+1)πb)4/(2n+1)πc)2/n(n+1)πd)4/n(n+1)πCorrect 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 If tan (cotx) = cot(tanx), then sin2x is equal toa)2/(2n+1)πb)4/(2n+1)πc)2/n(n+1)πd)4/n(n+1)πCorrect 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 If tan (cotx) = cot(tanx), then sin2x is equal toa)2/(2n+1)πb)4/(2n+1)πc)2/n(n+1)πd)4/n(n+1)πCorrect answer is option 'B'. Can you explain this answer?.
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