JAMB - Mathematics (1990 - No. 30)
If Cos \(\theta\) = \(\frac{12}{13}\). Find \(\theta\) + cos2\(\theta\)
\(\frac{169}{25}\)
\(\frac{25}{169}\)
\(\frac{169}{144}\)
\(\frac{144}{169}\)
설명
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 + \(\frac{144}{25}\)
= \(\frac{25 + 144}{25}\)
= \(\frac{169}{25}\)