To solve this problem, we can use the following trigonometric identities:

• sec(A) = 1/cos(A)
• cosec(A) = 1/sin(A)

Substituting these identities into the given equation, we get:

1/cos(A-12) = 1/sin(42)

Multiplying both sides of the equation by cos(A-12), we get:

1 = cos(A-12) * sin(42)

Using the angle addition formula for sin(x+y), we get:

1 = sin(A-12+42)

1 = sin(A+30)

The only acute angle whose sine is 1 is 90 degrees. Therefore, A+30 = 90 degrees. Subtracting 30 degrees from both sides of the equation, we get:

A = 90 degrees - 30 degrees

A = 60 degrees

Therefore, the value of A is 60 degrees.

Answer:

60 degrees

Step-by-step explanation:

sec (A - 12) = cosec 42
sec(A - 12) = cosec (90 - 48)

sec (A - 12) = sec 48  [since cosec(90 - m) = sec m; identity]

cancel sec and sec

A - 12 = 48--> A = 48 + 12 --> A=60 degrees