Question

Answer the following
If sec4A = cosec(A - 20), where 1 point
for A is an acute angle, find the
value of A.​

Answer 1

Given :

$\sf\sec(4A)=\csc(A-20)$ for A is an acute angle.

To Find :

The value of A

Formula's Used :

$\sf1)\sin(90-x)=\cos\:x$

$\sf2)\cos(90-x)=\sin\:x$

$\sf3)\tan(90-x)=\cot\:x$

$\sf4)\sec(90-x)=\csc\:x$

$\sf5)\cot(90-x)=\tan\:x$

$\sf6)\csc(90-x)=\sec\:x$

Solution :

We have to Find the value of A

$\sf\sec(4A)=\csc(A-20)$

Let A-20= x , then

$\sf\implies\sec(4A)=\csc(x)$

and

We know that sec(90-x)= csc (x) ,then

$\sf\implies\sec(4A)=\sec(90\degree-x)$

$\sf\implies\sec(4A)=\sec[90\degree-(A-20)]$

Now comparing on both sides , then

$\sf\:4A=90-A+20$

$\sf\implies\:4A+A=110$

$\sf\implies\:5A=110$

$\sf\implies\:A=\dfrac{110}{5}$

$\rm\implies\:A=22\degree$

Therefore, the value of A is 22°

Answer 2

Answer:

Correct Question :-

• If sec4A = cosec(A - 20°), where 4A is an acute angle, find the value of A.

Find Out :-

• What is the value of A.

Formula Required :-

✪ secΘ = cosec(90 - Θ) ✪

Solution :-

$\mapsto$ sec4A = cosec(A - 20°)

↦ cosec(90 - 4A) = cosec(A - 20°)[secΘ=cosec(90-Θ)]

By comparing angles, we get

↦ 90 - 4A = A - 20

↦ - 4A - A = - 20 - 90

↦ - 5A = - 110

↦ A = $\dfrac{-\: 110}{-\: 5}$

➠ A = 22°

$\therefore$ The value of A is 22°