Question

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

Answer 1

sec4A=cosec(A-20°)

cosec(90°-4A)=cosec(A-20°)-------[sec=cosec(90°-A)]

Comparing only angles

90°-4A=A-20°

-4A-A=-20-90

-5A=-110

A=110/5

A=22°

Answer 2

Hi,

______________________________

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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