cot^2(x)sec(x)-sec(x)=2cot^2(x)-2

Solución

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

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Pasos de solución

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

Restar

2 cot^{2} (x) - 2

de ambos lados

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

Factorizar

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

(cot (x) + 1) (cot (x) - 1) (sec (x) - 2) = 0

Resolver cada parte por separado

cot (x) + 1 = 0 or cot (x) - 1 = 0 or sec (x) - 2 = 0

cot (x) + 1 = 0 : x = \frac{3 π}{4} + πn

cot (x) - 1 = 0 : x = \frac{π}{4} + πn

sec (x) - 2 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combinar toda las soluciones

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

5 cot^{2} (x) - 2 csc (x) + 2 = 0

\frac{sin ( 7 5 ^{\circ} )}{101} = \frac{sin ( b )}{65}

3 tan (A) + 5 = 0

tan (2 x) = - \frac{( \frac{30 + 20}{2} )}{80}

15 sin^{2} (x) - 22 sin (x) + 8 = 0