What is the maximum value of $f (θ) = 12 sin θ + 5 cos θ - 4$ ?

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If $α$ and $β$ are acute, $sin α = \frac{3}{5}$ and $sin β = \frac{5}{13}$ , find $cos (α + β)$ .
If $α$ and $β$ are acute, $sin α = \frac{4}{5}$ and $sin β = \frac{12}{13}$ , find $cos (α + β)$ .
If $α$ and $β$ are acute, $sin α = \frac{3}{5}$ and $sin β = \frac{8}{17}$ , find $cos (α + β)$ .
If $α$ and $β$ are acute, $sin α = \frac{5}{13}$ and $sin β = \frac{7}{25}$ , find $cos (α + β)$ .
What is the maximum value of $f (θ) = 8 sin θ + 15 cos θ + 1$ ?
What is the eccentricity of the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1$ ?

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