Find all solutions of the equation in the interval 0 2tt Ent

Find all solutions of the equation in the interval [0, 2tt). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 3 cos^3 x = 3 cos x Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.) 64 cos^2 x - 16 = 0 Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval [0, 2pi). (Enter your answers as a comma-separated list.) 7 csc^2 x + 3.5 cot x - 35 = 0

Solution

3.

3cos³x = 3cosx

= 3cosx (1-cos²x) = 0

= 3cosx sin²x = 0

= cosx=0 or sin²x = 0

= x = (2n+1)/2 or n , n= 0,1,2,...

Also cos3x = 4cos³x - 3 cosx

implies that 3cos³x - 3cosx = cos3x - cos³x

4.

64 cos²x - 16 = 0

4cos²x - 1 = 0

cos²x = 1/4

cosx = +/- 1/2

x = 60^o, 300^o or 120^o, 240^o