Question

If sec 4 A = cosec (A − 15°), where 4 A is an acute angle, find the value of A.

Answer 1

\[\begin{array}{l}\sec4A = \ cosec(A -{15}^\circ ) \\ \end{array}\] 

\[\begin{array}{l}=> cosec( {90}^\circ - 4A) = \ cosec(A- {15}^\circ )[ \because \sec\theta = \ cosec ( {90}^\circ -\theta)] \\ \end{array}\] 

\[\begin{array}{l}{=>90}^\circ - 4A = A - {15}^\circ \\ \end{array}\] 

\[\begin{array}{l}{=>105}^\circ = 5A \\  \\ \end{array}\] 

\[=>A = \frac{{105}^\circ}{5} =  {21}^\circ\]