Solve the equation Enter your answers as a commaseparated li

Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.) sin x(sin x + 1) = 0 Find all solutions of the equation in the interval [0, 2 pi). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 7 cos^3 x = 7 cos x Find all solutions of the equation in the interval [0, 2 pi). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 9 sec^2 x - 9 = 0

Solution

8. sinx(sinx +1)=0

sin x=0   and sinx +1=0

sinx=0 and sinx=-1

Taking sin^-1on both sides

x=sin^-10        and    x=sin^-1-1

x=pi n             and   x= 2pi n -(pi/2),2pi n + (3pi/2)

x=pi n,2pi n -(pi/2),2pin + (3pi/2)

9. 7cos³x=7cos x

7cosx (cos²x-1)=0

cos x=0                 cos²x=1

cos x=0                cos x= +-1

Taking cos^-1on both sides

x= cos^-10                x= cos^-1(+-1)

x=pi n -(pi/2)          x= pi n , 2pi n + pi

x=pi n -(pi/2),pi n, 2pi n +pi