Question

if sec 2A = cosec (A-27) where 2A is an acute angle find the measure of <A​

Answer 1

sec2A=cosec(A-27°)
cosec(90°-2A)=cosec(A-27°)
where,90°-2A&A-27° are acute angles
90°-2A=A-27°
90°+27°=A+2A
117°=3A
117°/3=A
39°=A

the value of A is 39°

hope this answer will help you.

Answer 2

$sec2A=cosec(A-27$°$)$

$cosec(90$°$-2A)=cosec(A-27$°$)$

where, $90$° $-2A$ & $A-27$° are acute angles

$90$°$-2A=A-27$°

$90$°$+27$°$=A+2A$

$117$°$=3A$

$\frac{117}{3}=A$

$39$°$=A$

The value of $A$ is $39$°.