Question

How do you solve `cos(x-pi/6)=1+cos(x+pi/6)`?

Answer 1

Solution : `x= ((3pi)/2) =270^0`

Explanation:

`cos(x-pi/6) = 1 +cos (x+pi/6) or cos(x-pi/6) - cos (x+pi/6) =1 or cos x cos(pi/6) - sin x sin (pi/6) - (cosxcos(pi/6) + sin x sin (pi/6)) =1 or cancel(cos x cos(pi/6)) - sin x sin (pi/6) - cancel(cosxcos(pi/6)) - sin x sin (pi/6) =1 or -2 sinx sin (pi/6) =1 or - cancel2*1/cancel2*sinx=1` since `sin (pi/6)=1/2` or `sinx = -1 ; sin ((3pi)/2) = -1 :. sinx = sin ((3pi)/2) or x= ((3pi)/2) =270^0`[Ans]