Solve the following equations:
(i) `sin 5x-sin x=cos 3x` (ii) `2 cos^(2) theta+3 sin theta-3=theta`
(iii) `cos theta+cos 3 theta=2 cos 2 theta` (iv) `sin theta+sin 3 theta+sin 5 theta=0`
(v) `sin 2 theta-cos 2theta-sin theta+cos theta=0` (vi) `sin theta+cos theta=sqrt3`
(vii) `sin theta+sqrt3 cos theta=1` (viii) `cot theta+" cosec "theta=sqrt3`
`(ix) tan theta+tan (theta +pi/3) +tan (theta+(2pi)/(3))=sqrt3`
(x) `cos 2theta=(sqrt5+1)/(4)` (xi) `2 cos^(2) x -7 cos x+3=0`

Answer

(i) `x=(npi)/(2)+(-1)^(n) pi/(12)` (ii) `npi+(-1)^(n) pi//6, n in Z` (iii) `2npi, n in Z` (iv) `2npi pm 2pi//3` (v) `(2npi)/(3)-pi/6`
(vi) `pi/4(8n+1), n in Z` (vii) `2npi+pi//6 pm pi//3, n in Z` (viii) `2npi pm (2pi)/(3)-pi/3, n in Z` (ix) `sqrt3` (x) `npi pm pi/10, n in Z` (xi) `2npi pm pi//3, n in Z`