Find the principal and general solutions of the following equations: (i) tanx = √3 (ii) secx = 2 (iii) cotx = -√3 (iv) cosecx = 2

(i) tanx = √3 = tan(π/3) = tan(4π/3)
Hence principal solution of tanx = √3 are π/3 and 4π/3
tanx = √3 = tan(π/3)
Hence general solution is given by, x = nπ + π/3 where n ∈ Z
(ii) secx = 2 = sec(π/3) = sec(5π/3)
Hence principal solution of secx = 2 are π/3 and 5π/3
secx = 2 = sec(π/3)
Hence general solution is given by, x = 2nπ ± π/3, where n ∈ Z
(iii) cotx = -√3 = cot(5π/6) = cot(11π/6)
Hence principal value of cotx = -√3 are 5π/6 and 11π/6
cotx = -√3 = cot(5π/6)
Hence general solution is given by, x = nπ + 5π/6, where n ∈ Z
(iv) cscx = 2 = csc(π/6) = csc(5π/6)
Hence principal solution of cscx = 2 are π/6 and 5π/6
cscx = 2 = csc(π/6)
Hence general solution is given by, x = nπ + (-1)^n π/6, where n ∈ Z