Question

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

Answer 1

Here is is ur answer

Hi,

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This is related to Trigonometric Ratios of

Complementary Angles,

Two angles are said to be complementary

if their sum equals 90 degrees.

We know that ,

Cosec ( 90 - x ) = Sec x ----( 1 )

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Sec ( 4A ) = Cosec ( A - 20 )

Cosec ( 90- 4A ) = Cosec ( A - 20 )

[ from ( 1 ) ]

90 - 4A = A - 20

90 + 20 = A + 4A

110 = 5A

5A = 110

A = 110 / 5

A = 22

Therefore,

The required angle = A = 22 degrees.

I hope this helps you.

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Answer 2

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

$\huge\underbrace\mathrm{Solution}$

We know that sec 4A = cosec (90° – 4A)

To find the value of A, substitute the above equation in the given problem:

sin(A−20⁰)=cos(4A)

sin(A−20⁰)=cos(4A)sin(A−20⁰)=sin(90⁰−4A)

Hence,

A−20⁰=90⁰−4A

A−20⁰=90⁰−4A5A=110⁰

A−20⁰=90⁰−4A5A=110⁰A=22⁰