Question

Find all values of x in the interval [0, 2Ï] that satisfy the equation. (enter your answers as a comma-separated list.) 8 cos(x) + 4 sin(2x) = 0

Answer 1

The given equation is

`8cos(x)+ 4 sin(2x)=0`

Using the double angle formula of sin(2x),

`8cos(x) +4(2) sin(x)cos(x)=0`

`8cos(x)+ 8 sin(x) cos(x)=0`

Taking out 8 cos x

`8cos(x) (1+ sin(x)) =0`

`8 cos(x)=0 , 1+sin (x)=0 \\ 8cos (x)=0, sin(x)=-1 \\ cos(x)=0 , sin(x)=-1 \\ x = ( \pi)/(2) , ( 3 \pi)/(2)`

And that's the required answer.