If Cos \(\theta\) = \(\frac{12}{13}\). Find \(\theta\) + \(cos^2\theta\)

  • A \(\frac{169}{25}\)
  • B \(\frac{25}{169}\)
  • C \(\frac{169}{144}\)
  • D \(\frac{144}{169}\)
jamb 1990mathematics

The correct answer is A. \(\frac{169}{25}\)

Cos \(\theta\) = \(\frac{12}{13}\) x 2x + 12 2+ 12 = 13 2= 13 x 2x = 169- 144 = 25 x = 25 = 5 Hence, tan\(\theta\) = \(\frac{5}{12}\) and cos\(\theta\) = \(\frac{12}{13}\) 

If cos2If cos \(\theta\) = 1 + \(\frac{1}{tan^2\theta}\) = 1 + \(\frac{1}{\frac{(5)^2}{12}}\) = 1 + \(\frac{1}{\frac{25}{144}}\) = 1 + \(\frac{144}{25}\) = \(\frac{25 + 144}{25}\) = \(\frac{169}{25}\)

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