Use the information given below to find cos(alpha-beta). cos alpha=(3)/(5), with alpha in quadrant I tan beta=(3)/(4), with beta in quadrant III Give the exact answer, not a decimal approximation. cos(alpha-beta)=

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Apply cosine difference identity:  Use the cosine difference identity: cos(alpha - beta) = cos(alpha)cos(beta) + sin(alpha)sin(beta). Find sin(alpha):  Given cos(alpha) = 3/5. Since alpha is in quadrant I, sin(alpha) is positive. Use the Pythagorean identity sin^2(alpha) + cos^2(alpha) = 1 to find sin(alpha). Calculate sin(alpha):  Calculate sin(alpha): sin(alpha) = sqrt(1 - cos^2(alpha)) = sqrt(1 - (3/5)^2) = sqrt(1 - 9/25) = sqrt(16/25) = 4/5. Use tan(beta) to find sin(beta) and cos(beta):  Given tan(beta) = 3/4 and beta is in quadrant III, both sine and cosine are negative. Use tan(beta) = sin(beta)/cos(beta) to find sin(beta) and cos(beta). Find sin(beta) and cos(beta):  Find sin(beta) and cos(beta): sin(beta) = -3/5 and cos(beta) = -4/5, since the hypotenuse of the right triangle formed is 5 (3^2 + 4^2 = 5^2).

Use the information given below to find $\cos(\alpha-\beta)$ . $\newline$ $\cos \alpha=\frac{3}{5}$ , with $\alpha$ in quadrant I $\newline$ $\tan \beta=\frac{3}{4}$ , with $\beta$ in quadrant III $\newline$ Give the exact answer, not a decimal approximation. $\newline$ $\cos(\alpha-\beta)=$

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