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Popular >

3tan^2(480)

Solución

3 tan^{2} (48 0^{\circ})

Solución

9

Pasos de solución

3 tan^{2} (48 0^{\circ})

tan (48 0^{\circ}) = tan (12 0^{\circ})

tan (48 0^{\circ})

Reescribir

48 0^{\circ}

como

18 0^{\circ} \cdot 2 + 12 0^{\circ}

= tan (18 0^{\circ} 2 + 12 0^{\circ})

Utilizar la periodicidad de

tan

:

tan (x + 18 0^{\circ} \cdot k) = tan (x)

tan (18 0^{\circ} \cdot 2 + 12 0^{\circ}) = tan (12 0^{\circ})

= tan (12 0^{\circ})

= 3 tan^{2} (12 0^{\circ})

Re-escribir usando identidades trigonométricas:

tan^{2} (12 0^{\circ}) = sec^{2} (12 0^{\circ}) - 1

tan^{2} (12 0^{\circ})

Utilizar la identidad pitagórica:

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

tan^{2} (x) = sec^{2} (x) - 1

= sec^{2} (12 0^{\circ}) - 1

= 3 (sec^{2} (12 0^{\circ}) - 1)

Utilizar la siguiente identidad trivial:

sec (12 0^{\circ}) = - 2

sec (12 0^{\circ})

sec (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= - 2

= 3 ((- 2)^{2} - 1)

Simplificar

3 ((- 2)^{2} - 1) : 9

3 ((- 2)^{2} - 1)

Aplicar las leyes de los exponentes:

(- a)^{n} = a^{n},

si

n

es par

(- 2)^{2} = 2^{2}

= 3 (2^{2} - 1)

2^{2} = 4

= 3 (4 - 1)

Restar:

4 - 1 = 3

= 3 \cdot 3

Multiplicar los numeros:

3 \cdot 3 = 9

= 9

= 9

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