Fill in the blank to complete the trigonometric formula -8sin(u)_(x)=(8sin(u))/(1+cos(u))

To complete the trigonometric formula, we need to find the correct expression for the left-hand side of the equation.<br /><br />Given:<br />$-8sin(u)_{x}=\frac {8sin(u)}{1+cos(u)}$<br /><br />We can rewrite the left-hand side as:<br />$-8sin(u)_{x} = -8sin(u) \cdot \frac{1}{x}$<br /><br />Now, we need to find the value of $x$ that makes the left-hand side equal to the right-hand side.<br /><br />To do this, we can equate the two expressions and solve for $x$:<br />$-8sin(u) \cdot \frac{1}{x} = \frac{8sin(u)}{1+cos(u)}$<br /><br />Multiplying both sides by $x$:<br />$-8sin(u) = \frac{8sin(u)x}{1+cos(u)}$<br /><br />Dividing both sides by $8sin(u)$:<br />$-1 = \frac{x}{1+cos(u)}$<br /><br />Multiplying both sides by $(1+cos(u))$:<br />$-x = 1+cos(u)$<br /><br />Solving for $x$:<br />$x = -1-cos(u)$<br /><br />Therefore, the completed trigonometric formula is:<br />$-8sin(u)_{x}=\frac {8sin(u)}{1+cos(u)}$<br /><br />where $x = -1-cos(u)$.