Question

Solve `cos(3x)cos(x)+sin(3x)sin(x) = 0` ?

Answer 1

`x = pm pi/4+kpi, k=0,pm1,pm2,pm3,cdots`

Explanation:

Using

`cos(a-b)=cos(a)cos(b)+sin(a)sin(b)`

and making `a=3x` and `b=x` we have

`cos(3x)cos(x)+sin(3x)sin(x) = cos(2x)`

Now, solving

`cos(2x)=0` gives

`x = pm pi/4+kpi, k=0,pm1,pm2,pm3,cdots`