Question

6) Sabiendo que: Tgx + Ctgx = 4
Calcular:
K = Senx. COSX​

Answer 1

Hola.

Debemos considerar lo siguiente

$tan(x) = \frac{sen(x)}{cos(x)}$

$cot(x) = \frac{cos(x)}{sen(x)}$

$sen^{2}(x) + cos^{2}(x) = 1$

Resolvemos

$tan(x) + cot(x) = 4$

$\frac{sen(x)}{cos(x)} + \frac{cos(x)}{sen(x)} = 4$

$\frac{sen^{2}(x)+cos^{2}(x)}{sen(x)cos(x)}=4$

$\frac{1}{sen(x)cos(x)} = 4$

$1 = 4 * (sen(x)cos(x))$

$\frac{1}{4} = sen(x)cos(x)$

R. K = sen(x)cos(x) ===> K = 1/4

Un cordial saludo.