Question

if sec4A=cosec(A+18°) where 2A is an acute angle, then the value of A will be​

Answer 1

Answer:

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

Answer:

$\sec(4a) = \sec(90 - (a + 18))$

$4a = 90 - a - 18$

$5a = 72$

$a = \frac{72}{5}$

hope it helps