Can equation sin(x - 60) - cos(30 - x)=1 be written in the form cos x= k where k is a constant?

1 Answer
Feb 24, 2018

Given,

# sin(x-60) - cos (30-x)=1#

#=> sin x cos 60 - cos x sin 60 - cos 30 cos x - sin 30 sin x=1#

#=> (sin x)/2 - sqrt(3)/2 * cos x - sqrt(3)/2*cosx - (sinx)/2 =1#

# => -2 sqrt(3)/2*cos x=1#

# = cos x (-sqrt(3)) =1#

#=> cosx =-1/sqrt(3)=k#