Question

if sec 2A=cosec[A-42],where 2A is an acute angle,find the value ofcA

Answer 1

sec 2A = cosec(A-42°)

cosec(90°-2A) = cosec(A-42°)

90°-2A=A-42°

90°+42°=2A+A

3A= 132°

A=132°/3

A=44°

Answer 2

QUESTION :-

If sec 2A = cosec(A - 42°), where 2A is an acute angle, find the value of A.

SOLUTION :-

sec 2A = cosec(A - 42°)  

⇒cosec(90° - 2A) = cosec(A - 42°)

As cosec(90° - A) = secA, and vice-versa.

⇒ 90° - 2A = A - 42°

Same bases get cancelled.

⇒90° + 42° = A + 2A

⇒ 132°  = 3A

⇒A=132°/3

⇒ A=44°