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((tan^{(2(x))}(x)))/((cos(x)))>0

Solución

\frac{( tan ^{(2 (x))} ( x ) )}{( cos ( x ) )} > 0

Falso para todo x \in R

Pasos de solución

\frac{tan ^{2 x} ( x )}{cos ( x )} > 0

Periodicidad de

\frac{tan ^{2 x} ( x )}{cos ( x )} :

No periodico

La función

\frac{tan ^{2 x} ( x )}{cos ( x )}

no es periodica

= No periodico

Expresar con seno, coseno

\frac{tan ^{2 x} ( x )}{cos ( x )} > 0

Utilizar la identidad trigonométrica básica:

tan (x) = \frac{sin ( x )}{cos ( x )}

\frac{( \frac{s i n ( x )}{c o s ( x )} ) ^{2 x}}{cos ( x )} > 0

\frac{( \frac{s i n ( x )}{c o s ( x )} ) ^{2 x}}{cos ( x )} > 0

Simplificar

\frac{( \frac{s i n ( x )}{c o s ( x )} ) ^{2 x}}{cos ( x )} : \frac{sin ^{2 x} ( x )}{cos ^{2 x + 1} ( x )}

\frac{( \frac{s i n ( x )}{c o s ( x )} ) ^{2 x}}{cos ( x )}

(\frac{sin ( x )}{cos ( x )})^{2 x} = \frac{sin ^{2 x} ( x )}{cos ^{2 x} ( x )}

(\frac{sin ( x )}{cos ( x )})^{2 x}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{sin ^{2 x} ( x )}{cos ^{2 x} ( x )}

= \frac{\frac{s i n ^{2 x} ( x )}{c o s ^{2 x} ( x )}}{cos ( x )}

Aplicar las propiedades de las fracciones:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{sin ^{2 x} ( x )}{cos ^{2 x} ( x ) cos ( x )}

cos^{2 x} (x) cos (x) = cos^{2 x + 1} (x)

cos^{2 x} (x) cos (x)

Aplicar las leyes de los exponentes:

a^{b} \cdot a^{c} = a^{b + c}

cos^{2 x} (x) cos (x) = cos^{2 x + 1} (x)

= cos^{2 x + 1} (x)

= \frac{sin ^{2 x} ( x )}{cos ^{2 x + 1} ( x )}

= Sin soluci \overset{o}{ˊ} n para x \in R

Falso para todo x \in R

cot (2 x) \leq 3

5 - 5 cos^{2} (x) + 2 cos (x) \geq 0

sin (x) < 3

cos (\frac{π t}{2}) < 0

\frac{1}{( sin ( x ) ) ^{2}} < \frac{4}{3}, 0^{\circ} < x < 1 2^{\circ}