If Cos θ θ = 1213 12 13 . Find θ θ + cos2θ

Assessment: JAMB UTME - Mathematics - 1990 Subject: General Mathematics

Question 1 Report

If Cos $θ$ = $\frac{12}{13}$ . Find $θ$ + cos2 $θ$

\frac{169}{25}

\frac{25}{169}

\frac{169}{144}

\frac{144}{169}

Answer Details

Cos $θ$ = $\frac{12}{13}$
x2 + 122 = 132
x2 = 169- 144 = 25
x = 25
= 5
Hence, tan $θ$ = $\frac{5}{12}$ and cos $θ$ = $\frac{12}{13}$
If cos2 $θ$ = 1 + $\frac{1}{t a n^{2} θ}$
= 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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