Question

If sin (A + B) = 1 and cos (A − B) = 1, 0° ≤ (A + B) ≤ 90° and A > B, then find A and B.

Answer 1

Here, sin (A + B) = 1
⇒ sin (A+ B) = sin 90^o [∵ sin 90^o = 1]
⇒ A + B = 90^o​ ...(i)

Also, cos (A − B) = 1
⇒​ cos (A − B) = cos 0^o [∵​ cos 0^o = 1]
⇒ A − B = 0^o ...(ii)

Solving (i) and (ii), we get:
A = 45^o and B = 45^o