Find all solutions of the equation in the interval 0 2 Enter

Find all solutions of the equation in the interval [0, 2). (Enter your answers as a comma-separated list.)

cos(x+(3pi)/4)-cos(x-(3pi)/4)=1

Use a graphing utility to approximate the solutions of the equation in the interval [0, 2). (Enter your answers as a comma-separated list. Round your answers to four decimal places.)

sin ( x + / 2 ) + cos^2 x = 0

Solution

cos(x+(3pi)/4)=cos(x).cos((3pi)/4)-sin(x)sin((3pi/4))
cos(x-(3pi)/4)=cos(x).cos((3pi)/4)+sin(3pi/4)(sinx)

cos(x+(3pi)/4)-cos(x-(3pi)/4)=cos(x).cos((3pi)/4)-sin(x)sin((3pi/4))-(cos(x).cos((3pi)/4)+sin(3pi/4)(sinx))

cos(x).cos((3pi)/4)-sin(x)sin((3pi/4))-cos(x).cos((3pi)/4) -sin(3pi/4)(sinx)
-2sin(x).sin((3pi)/4)=1

sinx(sin(3pi/4)=-1/2

sinx (1/sqrt(2)) =-1/2

sinx =-1/sqrt(2)

x=5pi/4 and x=7pi/4