If sin (A – B) = 1/2 and cos (A + B) = 1/2 , 0 ≤ (A + B) ≤ 90 a

1.	If sin (A – B) = 1/2 and cos (A + B) = 1/2 , 0 ≤ (A + B) ≤ 90 and A > B, then find A and B.
Answer» Here, sin (A – B) = 1/2 ⇒ sin (A – B) = 30 [∵ sin 30 = 1/2 ] ⇒ (A – B) = 30 …….(i) Also, cos (A + B) = 1/2 ⇒ cos (A + B) = cos 60 [∵ cos 60 = 1/2 ] ⇒ A + B = 60 ….(ii) Solving (i) and (ii), we get: A = 45 and B = 15

If sin (A – B) = 1/2 and cos (A + B) = 1/2 , 0 ≤ (A + B) ≤ 90 and A > B, then find A and B.

Answer»

Here, sin (A – B) = 1/2

⇒ sin (A – B) = 30 [∵ sin 30 = 1/2 ]

⇒ (A – B) = 30 …….(i)

Also, cos (A + B) = 1/2

⇒ cos (A + B) = cos 60 [∵ cos 60 = 1/2 ]

⇒ A + B = 60 ….(ii)

Solving (i) and (ii), we get:

A = 45 and B = 15