Trigonometría Ejemplos

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

Step 1

Simplifica $\ln (\sqrt{1 - \sin (x)}) + \ln (\sqrt{1 + \sin (x)})$ .

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Usa las propiedades de los logaritmos del producto, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

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

Combina con la regla del producto para radicales.

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

Step 2

Grafica cada lado de la ecuación. La solución es el valor x del punto de intersección.

$x \approx - 49.52639732, - 47.86297493, - 46.38480467, - 44.72138228, - 43.24321201, - 41.57978962, - 40.10161936, - 38.43819697, - 36.9600267, - 35.29660432, - 33.81843405, - 32.15501166, - 30.6768414, - 29.01341901, - 27.53524874, - 25.87182636, - 24.39365609, - 22.7302337, - 21.25206344, - 19.58864105, - 18.11047078, - 16.4470484, - 14.96887813, - 13.30545574, - 11.82728548, - 10.16386309, - 8.68569282, - 7.02227044, - 5.54410017, - 3.88067778, - 2.40250751, - 0.73908513, 0.73908513, 2.40250751, 3.88067778, 5.54410017, 7.02227044, 8.68569282, 10.16386309, 11.82728548, 13.30545574, 14.96887813, 16.4470484, 18.11047078, 19.58864105, 21.25206344, 22.7302337, 24.39365609, 25.87182636, 27.53524874, 29.01341901, 30.6768414, 32.15501166, 33.81843405, 35.29660432, 36.9600267, 38.43819697, 40.10161936, 41.57978962, 43.24321201, 44.72138228, 46.38480467, 47.86297493, 49.52639732$

Step 3