sin^2(x)sec(x)cot(x)=(sqrt(3))/2

Solución

sin^{2} (x) sec (x) cot (x) = \frac{3}{2}

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

Pasos de solución

sin^{2} (x) sec (x) cot (x) = \frac{3}{2}

Restar

\frac{3}{2}

de ambos lados

sin^{2} (x) sec (x) cot (x) - \frac{3}{2} = 0

Simplificar

sin^{2} (x) sec (x) cot (x) - \frac{3}{2} : \frac{2 sin ^{2} ( x ) sec ( x ) cot ( x ) - 3}{2}

\frac{2 sin ^{2} ( x ) sec ( x ) cot ( x ) - 3}{2} = 0

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

2 sin^{2} (x) sec (x) cot (x) - 3 = 0

Expresar con seno, coseno

- 3 + 2 sin (x) = 0

Mover

3

al lado derecho

2 sin (x) = 3

Dividir ambos lados entre

2

sin (x) = \frac{3}{2}

Soluciones generales para

sin (x) = \frac{3}{2}

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

x, sin (y) = y cos (2 x)

2 sin (\frac{π}{2} - θ) = sin (- θ)

csc (x) cot (x) + cot (x) = 0

tan (x) = \frac{50}{36}

- 2 + cot (x) = - 3