Use a sum-to-product identity to find all solutions to the equation. sin 5x-sin
ID: 2912855 • Letter: U
Question
Use a sum-to-product identity to find all solutions to the equation. sin 5x-sin 2x 0 Describe in the most concise way possible the general solution to the given equation, where k is any integer. Select the correct choice below and fill in all the answer boxes within your choice (Simplify your answers. Type any angle measures in radians. Use the smallest non-negative angle possible when describing the general form of each angle. Use ascending order, entering the expression based on the smallest angle first. Type exact answers, using ? as needed. Use integers or fractions for any numbers in the expressions.) E. There is no solution.Explanation / Answer
sin 5x - sin 2x = 0
sin 5x - sin 2x = 2 cos ( 5x + 2x ) / 2 sin ( 5x - 2x )/2
2 cos (7x)/2 sin ( 3x) /2 = 0
cos 7x/2 = 0 , sin 3x /2 = 0
x= 2pi/3 + (4pi/3) k ,x= 0 + (4pi/3) k , x = 3pi/7 + ( 4pi/7)k ,x= pi/7 + (4pi/7) k
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