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Popular >

sec^2(arctan(2))+csc^2(arccot(3))

Solución

sec^{2} (arctan (2)) + csc^{2} (arccot (3))

Solución

15

Pasos de solución

sec^{2} (arctan (2)) + csc^{2} (arccot (3))

Re-escribir usando identidades trigonométricas:

sec (arctan (2)) = 5

sec (arctan (2))

Re-escribir usando identidades trigonométricas:

sec (arctan (2)) = 1 + 2^{2}

Usar la siguiente identidad:

sec (arctan (x)) = 1 + x^{2}

= 1 + 2^{2}

= 1 + 2^{2}

Simplificar

= 5

Re-escribir usando identidades trigonométricas:

csc (arccot (3)) = 10

csc (arccot (3))

Re-escribir usando identidades trigonométricas:

csc (arccot (3)) = \frac{1 + 3 ^{2}}{1 + 3 ^{2}}

Usar la siguiente identidad:

csc (arccot (x)) = \frac{1 + x ^{2}}{1 + x ^{2}}

= \frac{1 + 3 ^{2}}{1 + 3 ^{2}}

= \frac{1 + 3 ^{2}}{1 + 3 ^{2}}

Simplificar

= 10

= (5)^{2} + (10)^{2}

Simplificar

(5)^{2} + (10)^{2} : 15

(5)^{2} + (10)^{2}

(5)^{2} = 5

(5)^{2}

Aplicar las leyes de los exponentes:

a = a^{\frac{1}{2}}

= (5^{\frac{1}{2}})^{2}

Aplicar las leyes de los exponentes:

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

= 5^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiplicar fracciones:

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

= \frac{1 \cdot 2}{2}

Eliminar los terminos comunes:

2

= 1

= 5

(10)^{2} = 10

(10)^{2}

Aplicar las leyes de los exponentes:

a = a^{\frac{1}{2}}

= (1 0^{\frac{1}{2}})^{2}

Aplicar las leyes de los exponentes:

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

= 1 0^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiplicar fracciones:

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

= \frac{1 \cdot 2}{2}

Eliminar los terminos comunes:

2

= 1

= 10

= 5 + 10

Sumar:

5 + 10 = 15

= 15

= 15

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