Question

Ayudenme a resolver esta ecuacion Trigonometrica :( porfavor

Answer 1

Explicación paso a paso:

$\cos(x) - 4 \cos(x) \sin(x) = 0$

$\sin {}^{2} ( x) + \cos {}^{2} (x) = 1 \\ \sin {}^{2} (x) = 1 - \cos {}^{2} (x) \\ \sin(x) = \sqrt{1 - \cos {}^{2}(x) }$

$\cos(x) - 4 \cos(x) ( \sqrt{(1 - \cos {}^{2} (x)} ) = 0$

$\cos(x) (1 - 4( \sqrt{(1 - \cos {}^{2} (x) }) = 0$

$1 = 4 \sqrt{(1 - \cos {}^{2} (x) } ) \\ 1 {}^{2} = 16(1 - \cos {}^{2} (x)) \\ \frac{1}{16} = 1 - \cos {}^{2} (x) \\ \cos {}^{2} (x) = 1 - \frac{1}{16} \\ \cos {}^{2} (x) = \frac{15}{16} ... \cos(x) = + - \sqrt{ \frac{15}{16} } \\ \cos(x) = \frac{ \sqrt{15} }{4} ...x = 14.53grados \\ cos(x) = - \frac{ \sqrt{15} }{4} ....x = 165.47grados$

$\cos(x) = 0....x1 = 90 \: grados...270grados$