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General Solution of cos theta = cos alpha

If the angle ...

Question

If the angle A of a triangle ABC is given by the equation $5 cos A + 3 = 0$ , then $sin A$ and $tan A$ are the roots of the equation $15 x^{2} + 8 x - 16 = 0$

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Solution

$cos A = \frac{- 3}{5}$ $\Rightarrow sin A = \frac{4}{5}$

$tan A = - 4 / 3$
$15 x^{2} + 8 x - 16 = 0$
$15 x^{2} + 20 x - 12 x - 16 = 0$
$5 x (3 x + 4) - 4 (3 x + 4) = 0$
$x = - 4 / 3$ and $x = 4 / 5$

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