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العربية

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

Solution

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

Aucune solution pour x \in R

étapes des solutions

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

Soustraire

sec^{2} (x)

des deux côtés

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

Récrire en utilisant des identités trigonométriques

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

Utiliser l'identité hyperbolique:

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

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

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

Simplifier

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

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

Développer

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

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

Appliquer la loi de la distribution:

a (b - c) = ab - a c

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

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

Multiplier les nombres :

2 \cdot 1 = 2

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

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

Simplifier

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

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

Additionner les éléments similaires :

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

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

Grouper comme termes

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

2 - 2 = 0

= sec^{2} (x)

= sec^{2} (x)

= sec^{2} (x)

sec^{2} (x) = 0

Appliquer la règle

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

sec (x) = 0

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

Aucune solution pour x \in R

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

cot (x) = 1.2

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

sec (x) - tan (x) = 2

sin (\frac{2 π ( t + 101.75 )}{365}) = - 1