Question

If cosec (A + B) =1 and cosec (A - B) = 2,0° < (A + B) < 90° and A>B,
find,

(i) A and B
​

Answer 1

Answer:

A = 60° and B = 30°

Step-by-step explanation:

Given: cosec (A+B) = 1 , cosec (A-B) = 2 , 0° ≤ (A+B) ≤ 90° and A>B

To find: Values of A and B.

Solution:

cosec(A+B) = 1

⇒ cosec(A+B) = cosec 90°

⇒ A+B = 90°              --------[1]

Also, cosec(A-B) = 2

⇒ cosec(A-B) = cosec 30°

⇒ A-B = 30°              --------[2]

On solving equations [1] and [2], we get

A = 60° and B = 30°