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Domain and Range of Basic Inverse Trigonometric Functions

If cosA = 3...

Question

If $c o s A = \frac{3}{5}$ , find $9 c o t^{2} A - 1$ .

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Solution

$cos A = \frac{3}{5}$
$cot A = \frac{3}{4}$
$9 {cot}^{2} A - 1 = 9 \times (\frac{3}{4})^{2} - 1 = \frac{65}{16}$

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\frac{s i n A + c o s A}{s i n A - c o s A} = \frac{5}{3},

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