Read the following information and answer the two items that foll

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 Multiple Choice QuestionsMultiple Choice Questions

101.

Read the following information and answer the two items that follow : 

Let tan3AtanA = k where tan A ≠ 0 and K  13

For real values of tan A, K cannot lie between

  • 13 and 3

  • 12 and 2

  • 15 and 5

  • 17 and 7


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102.

Read the following information and answer the two items that follow :Let tan3AtanA = K, where tan A ≠ 0 and K = 13

What is tan2(A) equal to ? 

  • K + 13K + 1

  • K - 13K - 1

  • 3K - 1K - 1

  • k + 33k - 1


B.

K - 13K - 1

We have, tan3AtanA = K sin3A . cosAcos3A . sinA = K sin3A . cosA + cos3A . sinAsin3A . cosA - cos3A . sinA = K + 1K - 1 sin3A + Asin3A - A = K + 1K - 1 sin4Asin2A = K + 1K - 1 2cos2A = K + 1K - 1 21 - 2sin2A = K + 1K - 1 2 - 4sin2A = K + 1K - 1 4sin2A = 2 - K + 1K - 1 4sin2A =  2K - 2 - K - 1K + 1 = K - 3K - 1 sin2A =14K - 3K - 1and cos2A = 1 - 14K - 3K - 1

 cos2A = 4K - 4 - K + 3K - 1 = 3K - 1K - 1 tan2A = sin2A cos2A  = K - 3K - 13K - 1K - 1 = k - 33k - 1


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