Question on: JAMB Mathematics - 1990
If Cos \(\theta\) = \(\frac{12}{13}\). Find \(\theta\) + cos2\(\theta\)
A
\(\frac{169}{25}\)
B
\(\frac{25}{169}\)
C
\(\frac{169}{144}\)
D
\(\frac{144}{169}\)
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Correct Option: A
Cos \(\theta\) = \(\frac{12}{13}\)
x2 + 122 = 132
x2 = 169- 144 = 25
x = 25
= 5
Hence, tan\(\theta\) = \(\frac{5}{12}\) and cos\(\theta\) = \(\frac{12}{13}\)
If cos2\(\theta\) = 1 + \(\frac{1}{tan^2\theta}\)
= 1 + \(\frac{1}{\frac{(5)^2}{12}}\)
= 1 + \(\frac{1}{\frac{25}{144}}\)
= 1 + \(\frac{144}{25}\)
= \(\frac{25 + 144}{25}\)
= \(\frac{169}{25}\)
x2 + 122 = 132
x2 = 169- 144 = 25
x = 25
= 5
Hence, tan\(\theta\) = \(\frac{5}{12}\) and cos\(\theta\) = \(\frac{12}{13}\)
If cos2\(\theta\) = 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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