ill in the blank to complete the trigonometric formula. 8sin(u)+cos(u)_(times )=(8sin(u))/(1+cos(u))

To fill in the blank and complete the trigonometric formula, we need to find the value that should be placed in the blank to make the equation true.Given equation: To solve this, we can use the trigonometric identity .Let's rewrite the equation as: Now, let's multiply both sides of the equation by to eliminate the denominator on the right side: Expanding the left side, we get: Now, let's simplify the equation by combining like terms: Simplifying further, we get: Now, let's factor out from the first two terms: To make the equation true, the blank should be filled with .Therefore, the completed trigonometric formula is: So, the value that should be placed in the blank is .