Use the given information to find the exact function value. Given $$ \sec heta=\frac{13}{5} $$ and $$ heta $$ is in quadrant IV, find $$ \cos 2 heta $$ $$ -\frac{119}{169} $$ $$ \frac{120}{169} $$ $$ \frac{119}{169} $$ $$ -\frac{120}{169} $$

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Use the given information to find the exact function value. Given $$ \sec 	heta=\frac{13}{5} $$ and $$ 	heta $$ is in quadrant IV, find $$ \cos 2 	heta $$ $$ -\frac{119}{169} $$ $$ \frac{120}{169} $$ $$ \frac{119}{169} $$ $$ -\frac{120}{169} $$

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Step 1: Since $$\sec 	heta = \frac{13}{5}$$, we find $$\cos 	heta$$ as the reciprocal: $$\cos 	heta = \frac{5}{13}$$.

Step 2: Use the identity for $$\cos 2	heta$$: $$\cos 2	heta = 2\cos^2 	heta - 1$$.

Step 3: Calculate $$\cos^2 	heta$$: $$\cos^2 	heta = \left(\frac{5}{13}ight)^2 = \frac{25}{169}$$.

Step 4: Substitute $$\cos^2 	heta$$ into the identity: $$\cos 2	heta = 2 \cdot \frac{25}{169} - 1$$.

Step 5: Simplify: $$\cos 2	heta = \frac{50}{169} - 1 = \frac{50}{169} - \frac{169}{169} = \frac{50 - 169}{169} = \frac{-119}{169}$$.$$\frac{119}{169}$$

Use the given information to find the exact function value. Given \( \sec \theta=\frac{13}{5} \) and \( \theta \) is in quadrant IV, find \( \cos 2 \theta \) \( -\frac{119}{169} \) \( \frac{120}{169} \) \( \frac{119}{169} \) \( -\frac{120}{169} \)

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