Question

If sec2A = cosec(A - 42°), where 2A is an acute angle, then find the value of A.  

Answer 1

\[\sec2A = cosec\left( A - 42^\circ \right)\]

\[ \Rightarrow cosec\left( 90^\circ- 2A \right) = cosec\left( A - 42^\circ \right)\]

Comparing both sides, we get

\[90^\circ- 2A = A - 42^\circ\]

\[ \Rightarrow 2A + A = 90^\circ + 42^\circ\]

\[ \Rightarrow 3A = 132^\circ\]

\[ \Rightarrow A = \frac{132^\circ}{3}\]

\[ \therefore A = 44^\circ\]

Hence, the value of A is 44°