If 4A=cosec(A-20^ ), where 4A is an acute angles, find the value … - Vidyadip

Question

If $\sec4\text{A}=\text{cosec(A}-20^\circ),$ where 4A is an acute angles, find the value of A.

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Answer

Given: $\sec4\text{A}=\text{cosec}(\text{A}-20^\circ)$ and 4A is an acute angle
We have to find $ \theta$
Now
$\sec4\text{A}=\text{cosec}(\text{A}-20^\circ)$
$ \sec4\text{A}=\sec\big\{90^\circ-(\text{A}-20^\circ)\big\}$
$ \sec4\text{A}=\sec(90^\circ-\text{A}+20^\circ)$
$ \sec4\text{A}=\sec(110^\circ-\text{A})$
$ 5\text{A}=110^\circ$
$ \text{A}=22^\circ$
Hence the value of A is 22º

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