Question

(Furg-RS) Determine a alternativa que indica o valor da expressão z =
$cos(x) + \tan(x) \\ sec(x) + cotg(x)$

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Answer 1

Resposta:

letra d

Explicação passo-a-passo:

$z = \frac{\cos(x)\:+\:\tan(x)}{\sec(x)\:+\:\cot(x)}$

$z = \frac{\cos(x)\:+\:\frac{\sin(x)}{\cos(x)}}{\frac{1}{\cos(x)}\:+\:\frac{\cos(x) }{\sin(x)}}$

$z = \frac{\frac{\cos^{2}(x)\:+\:\sin(x)}{\cos(x)}}{\frac{\sin(x)\: +\: \cos^{2}(x)}{\cos(x)\sin(x)}}$

$z = \frac{\cos^{2}(x)\:+\:\sin(x)}{\cos(x)}\frac{\cos(x)\sin(x)}{\sin(x)\:+\:\cos ^{2}(x)}$

$z = \sin(x)$

$z = \frac{3}{4}$