Question

If sec 4A = cosec (A - 20)° , where 4A is an acute angle , find the value of A

Answer 1

We need to find A.

$step \: by \: step \: explanation$
$sec \: 4a = cosec \: (a - 20) \\ cosec(90 - 4a) = \\ cosec(a - 20) \\ cosec \: gets \: eliminated \\ thus \: 90 - 4a = a - 20 \\ 90 + 20 = 4a + a \\ 110 = 5a \\ a = 20 \\ value \: of \: a \: is \: 20.$

Answer 2

$\huge\sf{Given\:that,}$

$\longrightarrow$$\large\sf{sec\:4A=cosec(A-20°)}$

$\longrightarrow$$\large\sf{cosec(90°-4A))=cosec(A-20°)}$

$\longrightarrow$$\large\sf{90°-4A=A-20°}$

$\longrightarrow$$\large\sf{110°=5A}$

$\longrightarrow$$\large\sf{A=22°}$