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Populaire >

cos^2(x)=((6k-7))/7

Solution

cos^{2} (x) = \frac{( 6 k - 7 )}{7}

x = arccos (\frac{6 k - 7}{7}) + 2 πn, x = - arccos (\frac{6 k - 7}{7}) + 2 πn, x = arccos (- \frac{6 k - 7}{7}) + 2 πn, x = - arccos (- \frac{6 k - 7}{7}) + 2 πn

étapes des solutions

cos^{2} (x) = \frac{( 6 k - 7 )}{7}

Résoudre par substitution

cos^{2} (x) = \frac{6 k - 7}{7}

Soit :

cos (x) = u

u^{2} = \frac{6 k - 7}{7}

u^{2} = \frac{6 k - 7}{7} : u = \frac{6 k - 7}{7}, u = - \frac{6 k - 7}{7}

u^{2} = \frac{6 k - 7}{7}

Pour

x^{2} = f (a)

les solutions sont

x = f (a), - f (a)

u = \frac{6 k - 7}{7}, u = - \frac{6 k - 7}{7}

Remplacer

u = cos (x)

cos (x) = \frac{6 k - 7}{7}, cos (x) = - \frac{6 k - 7}{7}

cos (x) = \frac{6 k - 7}{7}, cos (x) = - \frac{6 k - 7}{7}

cos (x) = \frac{6 k - 7}{7} : x = arccos (\frac{6 k - 7}{7}) + 2 πn, x = - arccos (\frac{6 k - 7}{7}) + 2 πn

cos (x) = \frac{6 k - 7}{7}

Appliquer les propriétés trigonométriques inverses

cos (x) = \frac{6 k - 7}{7}

Solutions générales pour

cos (x) = \frac{6 k - 7}{7}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

x = arccos (\frac{6 k - 7}{7}) + 2 πn, x = - arccos (\frac{6 k - 7}{7}) + 2 πn

x = arccos (\frac{6 k - 7}{7}) + 2 πn, x = - arccos (\frac{6 k - 7}{7}) + 2 πn

cos (x) = - \frac{6 k - 7}{7} : x = arccos (- \frac{6 k - 7}{7}) + 2 πn, x = - arccos (- \frac{6 k - 7}{7}) + 2 πn

cos (x) = - \frac{6 k - 7}{7}

Appliquer les propriétés trigonométriques inverses

cos (x) = - \frac{6 k - 7}{7}

Solutions générales pour

cos (x) = - \frac{6 k - 7}{7}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

x = arccos (- \frac{6 k - 7}{7}) + 2 πn, x = - arccos (- \frac{6 k - 7}{7}) + 2 πn

x = arccos (- \frac{6 k - 7}{7}) + 2 πn, x = - arccos (- \frac{6 k - 7}{7}) + 2 πn

Combiner toutes les solutions

x = arccos (\frac{6 k - 7}{7}) + 2 πn, x = - arccos (\frac{6 k - 7}{7}) + 2 πn, x = arccos (- \frac{6 k - 7}{7}) + 2 πn, x = - arccos (- \frac{6 k - 7}{7}) + 2 πn

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

cos (2 x) - cos (- x) = 0

cos (3 x) = sin (x)

4 tan^{2} (θ) = 12, 0 \leq θ < 2 π

cos^{2} (x) = 1 - 2 sin^{2} (x)