The expression represents the ratio of the sine function raised to the nth power to the sum of the sine function raised to the nth power and the cosine function raised to the nth power.
The expression can be simplified by factoring out sin^n(x) from the numerator and denominator, leaving sin^n(x) as the common factor. This results in the simplified expression of 1/(1+cos^n(x)).
The domain of the expression is all real numbers except for values of x that make the denominator equal to 0, which would result in an undefined expression. This occurs when x is equal to (2k+1)π/2, where k is any integer.
The value of n affects the steepness of the graph. As n increases, the graph becomes steeper and approaches a vertical asymptote at x=0 and x=π/2. As n decreases, the graph becomes flatter and approaches a horizontal asymptote at y=1.
Yes, the expression can be negative depending on the values of x and n. For example, if x=π/4 and n=2, the expression would be equal to -0.5. However, if x=π/3 and n=3, the expression would be positive. The sign of the expression depends on the values of x and n, but it is not always negative.