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ACT Exam  >  ACT Questions  >  Which of the following is the correct relatio... Start Learning for Free
Which of the following is the correct relation between A and B, if A = tan 110 . tan 290, and B = 2 cot 610 . cot 790?
  • a)
    A = B
  • b)
    A = -B
  • c)
    A = 2B
  • d)
    2A = B
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Which of the following is the correct relation between A and B, if A =...
Given A = tan 110 . tan 290, and B = 2 cot 610 . cot 790
A / B = tan 110 . tan 290 / 2 cot 610 . cot 790
= [tan 110 . tan 290] / [2 cot (900 - 290) . cot (900 - 110)]
= tan 110 . tan 290 / 2 tan 110 . tan 290
= 1/2
So, A/B = 1/2
Or, 2A = B
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Most Upvoted Answer
Which of the following is the correct relation between A and B, if A =...
Given A = tan 110 . tan 290, and B = 2 cot 610 . cot 790
A / B = tan 110 . tan 290 / 2 cot 610 . cot 790
= [tan 110 . tan 290] / [2 cot (900 - 290) . cot (900 - 110)]
= tan 110 . tan 290 / 2 tan 110 . tan 290
= 1/2
So, A/B = 1/2
Or, 2A = B
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Community Answer
Which of the following is the correct relation between A and B, if A =...
Explanation:

Given:
A = tan 110 * tan 290
B = 2 cot 610 * cot 790

Using trigonometric identities:
1. tan (90° + x) = -cot x
2. cot (90° + x) = -tan x

Calculating A:
tan 110 = tan (90 + 20) = -cot 20
tan 290 = tan (90 + 200) = -cot 200
A = (-cot 20) * (-cot 200) = cot 20 * cot 200

Calculating B:
cot 610 = cot (90 + 520) = -tan 520
cot 790 = cot (90 + 700) = -tan 700
B = 2 * (-tan 520) * (-tan 700) = 2 * tan 520 * tan 700

Comparing A and B:
A = cot 20 * cot 200
2A = 2 * cot 20 * cot 200 = 2 * (-tan 20) * (-tan 200) = 2 * tan 20 * tan 200
B = 2 * tan 520 * tan 700
Therefore, 2A = B
Therefore, the correct relation between A and B is:
2A = B
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Which of the following is the correct relation between A and B, if A = tan 110. tan 290, and B = 2 cot 610. cot 790?a)A = Bb)A = -Bc)A = 2Bd)2A = BCorrect answer is option 'D'. Can you explain this answer?
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