Question

Reduce la siguiente expresión: F = (cos 180° + csc 90° + 2sec 360°):(1 – sen3π/2)

Answer 1

Hola!

Respuesta:

F = 1

Explicación paso a paso:

∆) Solución:

$F = \cos</strong><strong>(</strong><strong>180</strong><strong>)</strong><strong> </strong><strong>+</strong><strong> \csc</strong><strong>(</strong><strong>90</strong><strong>)</strong><strong> + 2 \sec</strong><strong>(</strong><strong>360</strong><strong>)</strong><strong> \div (1 - \sin \frac{3\pi}{2} ) \\ F = \frac{ ( \cos</strong><strong>(</strong><strong>180</strong><strong>)</strong><strong> + \csc</strong><strong>(</strong><strong>90</strong><strong>)</strong><strong> + 2 \sec</strong><strong>(</strong><strong> </strong><strong>360</strong><strong>)</strong><strong>)}{(1 - \sin \frac{3\pi}{2} )} \\ F = \frac{ ( - 1 + 1 + 2(1))}{(1 - \sin</strong><strong>(</strong><strong>270</strong><strong>)</strong><strong>) } \\ F = \frac{2}{1 - ( - 1)} \\ F = \frac{2}{2} \\ F = 1$

∆) Recordemos:

$</strong><strong>\</strong><strong>p</strong><strong>i</strong><strong> </strong><strong>=</strong><strong> </strong><strong>1</strong><strong>8</strong><strong>0</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\cos</strong><strong>(</strong><strong>180</strong><strong>)</strong><strong> </strong><strong>= - 1</strong><strong> </strong><strong>\\ \csc</strong><strong>(</strong><strong>90</strong><strong>)</strong><strong> = + 1 \\ \sec</strong><strong>(</strong><strong>3</strong><strong>60</strong><strong>)</strong><strong> = + 1 \\ \sin</strong><strong>(</strong><strong>270</strong><strong>)</strong><strong> = - 1$