The graph with the equation y cos 7x cos 9xsin 7x sin 9x

The graph with the equation y = cos 7x - cos 9x/sin 7x + sin 9x is shown in a [0, 2pi, pi] by [- 2, 2, 1] viewing rectangle. Describe the graph using another equation. Verify that the two equations are equivalent. Write another equation of the given graph. (Type an equation using x as the variable.) To verify that the two equations are equal, start with the numerator of the right side and apply the appropriate sum-to-product formula. cos 7x - cos 9x = (Do not simplify.) Now use the sum-to-product formula on the denominator of the right side, sin 7x + sin 9x = (Do not simplify.) In the numerator and denominator, substitute the expressions found in previous steps. Then simplify the angles and divide out the common factor of the expression. Use the even-odd identity. (Simplify your answer.) The fraction from the previous step then simplifies to answer of part a using what?

Solution

a) y = tan(x)

c) cos(7x) - cos(9x) = 2sin(8x)sin(x)

d) sin(7x) + sin(9x) = 2sin(8x)cos(x)

=> RHS = [sin(8x)sin(x)]/[2sin(8x)cos(x)] = sin(x)/cos(x) = tan(x)