Question

if sec4A = cosec(A-20) where 4A is an acute angle find the value of A​

Answer 1

• sec 4A = sec ( 90° - A + 20° )
• 4A = 110-A
• 5A = 110°
• A = 22°
• VALUE OF A = 22°
• Formula used : secA = cosec(90°-A)

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Answer 2

$\large\bf{\underline{\underline{Solution :-}}}$

$\underline{\boxed{\sf\purple{sec \:4A\: =\: cosec\: (90° - 4A) \:= \:cosec \:(A - 20°)}}}$

$\large\bf{\underline{\underline{Therefore,}}}$

$\longrightarrow$$\bf{90° – 4A = A - 20°}$

$\longrightarrow$$\bf{110°– 4A = A}$

$\longrightarrow$$\bf{5A = 110°}$

$\sf\longrightarrow \: A= \cancel\dfrac {110°} {5}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\pink{\bigstar}★ \large\underline{\boxed{\bf\purple{A = 22°}}}$

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Refer the attachment for better understanding :)