`a) sin (3x - 50^0) = (-\sqrt{2})/2`
`<=> sin (3x - 50^0) = sin (-45^0)`
`<=>` \(\left[ \begin{array}{l}3x - 50^0 = -45^0 + k360^0\\3x - 50^0 = 225^0 + k360^0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x = \dfrac{5}{3}^0 + k120^0\\x = \dfrac{275}{3}^0 + k120^0\end{array} \right.\) `(k ∈ ZZ)`
`b) 2cos (x - π/4) = 1`
`<=> cos (x - π/4) = 1/2`
`<=> cos (x - π/4) = cos (π/3)`
`<=>` \(\left[ \begin{array}{l}x - \dfrac{π}{4} = \dfrac{π}{3} + k2π\\x - \dfrac{π}{4} = -\dfrac{π}{3} + k2π\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x = \dfrac{7π}{12} + k2π\\x = \dfrac{-π}{12} + k2π\end{array} \right.\) `(k ∈ ZZ)`
`c) tan (π/12 + 12x) = sqrt{3}`
`<=> π/12 + 12x = π/3 + kπ`
`<=> 12x = π/4 + kπ`
`<=> x = π/48 + k(π)/12` `(k ∈ ZZ)`
`d) 3cot (5x - 1) - 1 = 0`
`<=> cot (5x - 1) = 1/3`
`<=> 5x - 1 = arctan (1/3) + kπ`
`<=> 5x = 1 + arctan (1/3) + kπ`
`<=> x = 1/5 + (arctan (1/3))/5 + k(π)/5` `(k ∈ ZZ)`
`e) cos (x + 30^0) = (-\sqrt{3})/2`
`<=> x + 30^0 = 150^0 + k360^0`
`<=> x = 120^0 + k360^0` `(k ∈ ZZ)`
