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(1+tan(x))^2+(1-tan(x))^2=sec^2(x)

Solución

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

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

Pasos de solución

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

Restar

sec^{2} (x)

de ambos lados

2 tan^{2} (x) - sec^{2} (x) + 2 = 0

Re-escribir usando identidades trigonométricas

2 - sec^{2} (x) + 2 tan^{2} (x)

Utilizar la identidad pitagórica:

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

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

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

Simplificar

2 - sec^{2} (x) + 2 (sec^{2} (x) - 1) : sec^{2} (x)

2 - sec^{2} (x) + 2 (sec^{2} (x) - 1)

Expandir

2 (sec^{2} (x) - 1) : 2 sec^{2} (x) - 2

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

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 2, b = sec^{2} (x), c = 1

= 2 sec^{2} (x) - 2 \cdot 1

Multiplicar los numeros:

2 \cdot 1 = 2

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

= 2 - sec^{2} (x) + 2 sec^{2} (x) - 2

Simplificar

2 - sec^{2} (x) + 2 sec^{2} (x) - 2 : sec^{2} (x)

2 - sec^{2} (x) + 2 sec^{2} (x) - 2

Sumar elementos similares:

- sec^{2} (x) + 2 sec^{2} (x) = sec^{2} (x)

= 2 + sec^{2} (x) - 2

Agrupar términos semejantes

= sec^{2} (x) + 2 - 2

2 - 2 = 0

= sec^{2} (x)

= sec^{2} (x)

= sec^{2} (x)

sec^{2} (x) = 0

Aplicar la regla

x^{n} = 0 \Rightarrow x = 0

sec (x) = 0

sec (x) \leq - 1 or sec (x) \geq 1

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

tan (x) = - \frac{2}{2}

cot (x) = 1.2

cos (\frac{3}{2} π - x) + sin (4 x) = 0

tan (x) = \frac{30}{100}

cos (θ) = - \frac{53}{8}