1 cos2x12 2 cos4x1 3 cotx2sqrt3 4 csc3x2 5 cosx3sqrt32 6 cot

1. cos(2x)=1/2

2. cos(4x)=-1

3. cot(x/2)=sqrt(3)

4. csc(3x)=2

5. cos(x/3)=-sqrt(3)/2

6. cot(5x)=-sqrt(3)

answer in form x=___+___pi*n

1. cos(2x)=1/2

2x = cos^-1(1/2)

2x = pi/3 ---> x = pi/6

2x = 2pi -pi/3 = 5pi/3

x = 5pi/6

Solution : x = pi/6 +2pi*n

x = 5pi/6 +2pi*n

2. cos(4x)=-1

4x = cos^-1(-1) =pi-pi/4 , pi+pi/4

x = 3pi/16 , x = 5pi/16

Solution : x = 3pi/16 +2pi*n

x = 5pi/16 +2pi*n

3. cot(x/2)=sqrt(3)

tan(2x) = 1/sqrt3

2x = pi/6 , 7pi/6

x = pi/12 , 7pi/12

Gen solution : x = pi/12 +pi*n ; x = 7pi/12 +pi*n

4. csc(3x)=2

sin(3x) =1/2

3x = pi/6 , 5pi/6

x = pi/18 , 5pi/18

Gen solution : x = pi/18 +2pi*n

x = 5pi/18 +2pi*n