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: Option A
Explanation
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^2theta})
= 1 + (frac{1}{frac{(5)^2}{12}})
= 1 + (frac{1}{frac{25}{144}})
= 1 + (frac{144}{25})
= (frac{25 + 144}{25})
= (frac{169}{25})