Question

If sin(A + B) = cos(A - B) = 1/√2, then find A and B, where 0° < A + B < 90° and A > B​

Answer 1

Step-by-step explanation:

sin (A + B)= 1 or sin (A + B) = sin 90° [As sin 90° = 1] A + B = 90° …

(1) Again, Cos(A-B) = 1 = cos 0°

A – B = 0 …(2)

Adding (1) and (2),

we get

2A = 90° or A = 45°

Putting A = 45° in (1)

we get

45° + B = 90° or B = 45°

Hence, A = 45° and B = 45°.