If Cos \(\theta\) = \(\frac{12}{13}\). Find \(\theta\) + cos2\(\theta\)

A.

\(\frac{169}{25}\)

B.

\(\frac{25}{169}\)

C.

\(\frac{169}{144}\)

D.

\(\frac{144}{169}\)

Correct answer is 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 + \(\frac{144}{25}\)

= \(\frac{25 + 144}{25}\)

= \(\frac{169}{25}\)