Question

cos (theta-60)=3 cos theta find the general solution

Answer 1

cos (theta-60)=3 cos theta
cos theta cos 60 + sin theta son 60 = 3 cos theta

as cos 60 = 1/2 and sin 60 = sqrt 3/2

(1/2) cos theta + sqrt 3 / 2 sin theta = 3 cos theta

cos theta +sqrt 3 sin theta = 6 cos theta

Answer 2

5 cos theta - sqrt 3 sin theta = 0
5 cos theta = sqrt 3 sin theta

squaring both sides we get

25 cos ^2 theta = 3 sin^2 theta

divide both sides by cos ^2 theta we get
25 = 3 (sin ^2 theta )/(cos^ theta)

25/3 = tan ^2 theta

now solve for theta