solvefor x,sin(x)+cot(x)cos(x)= 1/f

Solución

resolver para

x, sin (x) + cot (x) cos (x) = \frac{1}{f}

x = arcsin (f) + 2 πn, x = π + arcsin (- f) + 2 πn

Pasos de solución

sin (x) + cot (x) cos (x) = \frac{1}{f}

Restar

\frac{1}{f}

de ambos lados

sin (x) + cot (x) cos (x) - \frac{1}{f} = 0

Simplificar

sin (x) + cot (x) cos (x) - \frac{1}{f} : \frac{f sin ( x ) + f cot ( x ) cos ( x ) - 1}{f}

\frac{f sin ( x ) + f cot ( x ) cos ( x ) - 1}{f} = 0

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

f sin (x) + f cot (x) cos (x) - 1 = 0

Re-escribir usando identidades trigonométricas

- 1 + \frac{f}{sin ( x )} = 0

Multiplicar ambos lados por

sin (x)

- sin (x) + f = 0

Mover

f

al lado derecho

- sin (x) = - f

Dividir ambos lados entre

- 1

sin (x) = f

Aplicar propiedades trigonométricas inversas

x = arcsin (f) + 2 πn, x = π + arcsin (- f) + 2 πn

\frac{1}{sin ( x )} = 2

tan (x) csc (x) - 2 tan (x) = 0

1 - 2 sin (θ) = 0

cos (2 θ) + 3 cos (θ) = 4

0 = 2 cos (x) - 3 sin (x)