If sin (A – B) = 1/2, cos (A + B) = 1/2, 0° < A + B ≤ 90°, A > B, find A and B
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Given that
sin (A – B) = 1/2
⇒ A - B = 30° (as sin 30° = 1/2)
cos (A + B) = 1/2
⇒ A+B = 60° (as cos 60° = 1/2)
Now solve these two equations to find out A and B.
Add them,
2A = 90°
⇒ A = 90°/2 = 45
B = 60° - A = 60° - 45° = 15°
So A = 45° and B=15°
sin (A – B) = 1/2
⇒ A - B = 30° (as sin 30° = 1/2)
cos (A + B) = 1/2
⇒ A+B = 60° (as cos 60° = 1/2)
Now solve these two equations to find out A and B.
Add them,
2A = 90°
⇒ A = 90°/2 = 45
B = 60° - A = 60° - 45° = 15°
So A = 45° and B=15°
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