Question

if sec 5A = codec (A+36) where 5A is acute find A

Answer 1

sec 5A = cosec ( A + 36)

As A is acute angle then:

cosec ( 90 - 5A) = cosec ( A + 36 ) (Cosec and cosec CANCEL)

90 - 5A = A + 36

90 - 36 = A + 5A

54 = 6A

54/6 = A

9 = A


So the value of A = 9 degree


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Answer 2

We have, 

Sec 5A= Cosec (A+36)

Converting Sec to Cosec

Cosec (90- 5A)= Cosec (A+ 36) {Cancel Cosec on both sides}

(90- 5A) = (A+36) 

Solving the equation, we get:

⇒90- 5A= A+ 36

⇒90-36= A + 5A

⇒ 54 = 6A

⇒ A= 54/6

⇒ A= 9

Hence, A= 9°