English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

cos^2(x)=(1-tan^2(x))/(sec^2(x))

Solution

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

x = πn

Degrés

x = 0^{\circ} + 18 0^{\circ} n

étapes des solutions

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

Soustraire

\frac{1 - tan ^{2} ( x )}{sec ^{2} ( x )}

des deux côtés

cos^{2} (x) - \frac{1 - tan ^{2} ( x )}{sec ^{2} ( x )} = 0

Simplifier

cos^{2} (x) - \frac{1 - tan ^{2} ( x )}{sec ^{2} ( x )} : \frac{cos ^{2} ( x ) sec ^{2} ( x ) - 1 + tan ^{2} ( x )}{sec ^{2} ( x )}

cos^{2} (x) - \frac{1 - tan ^{2} ( x )}{sec ^{2} ( x )}

Convertir un élément en fraction:

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

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

Puisque les dénominateurs sont égaux, combiner les fractions:

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

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

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

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

Distribuer des parenthèses

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

Appliquer les règles des moins et des plus

- (- a) = a, - (a) = - a

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

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

\frac{cos ^{2} ( x ) sec ^{2} ( x ) - 1 + tan ^{2} ( x )}{sec ^{2} ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

cos^{2} (x) sec^{2} (x) - 1 + tan^{2} (x) = 0

Récrire en utilisant des identités trigonométriques

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

Utiliser l'identité trigonométrique de base:

cos (x) = \frac{1}{sec ( x )}

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

Simplifier

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

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

(\frac{1}{sec ( x )})^{2} sec^{2} (x) = 1

(\frac{1}{sec ( x )})^{2} sec^{2} (x)

(\frac{1}{sec ( x )})^{2} = \frac{1}{sec ^{2} ( x )}

(\frac{1}{sec ( x )})^{2}

Appliquer la règle de l'exposant:

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

= \frac{1 ^{2}}{sec ^{2} ( x )}

Appliquer la règle

1^{a} = 1

1^{2} = 1

= \frac{1}{sec ^{2} ( x )}

= \frac{1}{sec ^{2} ( x )} sec^{2} (x)

Multiplier des fractions:

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

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

Annuler le facteur commun :

sec^{2} (x)

= 1

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

Grouper comme termes

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

- 1 + 1 = 0

= tan^{2} (x)

= tan^{2} (x)

tan^{2} (x) = 0

Appliquer la règle

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

tan (x) = 0

Solutions générales pour

tan (x) = 0

Tableau de périodicité

tan (x)

avec un cycle

πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

Résoudre

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

sin^{2} (x) - 3 cos (x) - 4 = 0

tan^{2} (x) + sec (x) = 5

4 sin^{5} (x) = 3

cos (\frac{x}{2}) = 0.5

sin (x + 6 0^{\circ}) = 2 cos (x)