If sec(4x - 50°) = cosec(50° - x), then the value of x is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{sec}}\left( {4x - {{50}^ \circ }} \right) = {\text{cosec}}\left( {{{50}^ \circ } - x} \right) \cr & {\text{sec}}\left( {4x - {{50}^ \circ }} \right) = {\text{cosec}}\left( {{{90}^ \circ } - \left( {{{40}^ \circ } + x} \right)} \right) \cr & {\text{sec}}\left( {4x - {{50}^ \circ }} \right) = {\text{sec}}\left( {{{40}^ \circ } + x} \right) \cr & 4x - {50^ \circ } = {40^ \circ } + x \cr & 3x = {90^ \circ } \cr & x = {30^ \circ } \cr} $$