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प्रश्न
If sec2A = cosec(A - 42°), where 2A is an acute angle, then find the value of A.
उत्तर
\[\sec2A = cosec\left( A - 42^\circ \right)\]
\[ \Rightarrow cosec\left( 90^\circ- 2A \right) = cosec\left( A - 42^\circ \right)\]
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°
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