If sin(A + B) = cos(A - B) = \(\frac{\sqrt 3}{2}\) and A and B are a

1.	If sin(A + B) = cos(A - B) = \(\frac{\sqrt 3}{2}\) and A and B are acute angle. The measures of angles A and B (in degrees) will be:1. A = 60 and B = 302. A = 45 and B = 153. A = 45 and B = 454. A = 15 and B = 45
Answer» Correct Answer - Option 2 : A = 45 and B = 15 Given: sin(A + B ) = cos(A - B) = √3/2 Calculation: sin(A + B) = √3/2 ⇒ sin(A + B )= sin60° ⇒ A + B = 60° ….(i) And, cos(A - B) = √3/2 ⇒ cos(A - B) = cos30° ⇒ A – B = 30° ….(ii) Adding (i) and (ii) We get, 2A = 90° ⇒ A = 45° Putting in (i) We get, ⇒ 45° + B = 60° ⇒ B = 15° ∴ A and B are 45°and 15° Short trick sin(A + B )= sin60 cos(A - B) = cos30° So, A + B = 60° and A – B = 30° Takes oprtion he different is 30° and sum is 60° So option B and D are satisfy but in option D difference is negative Then option B is right A= 45° and B = 15°

If sin(A + B) = cos(A - B) = \(\frac{\sqrt 3}{2}\) and A and B are acute angle. The measures of angles A and B (in degrees) will be:1. A = 60 and B = 302. A = 45 and B = 153. A = 45 and B = 454. A = 15 and B = 45

Answer» Correct Answer - Option 2 : A = 45 and B = 15

Given:

sin(A + B ) = cos(A - B) = √3/2

Calculation:

sin(A + B) = √3/2

⇒ sin(A + B )= sin60°

⇒ A + B = 60° ….(i)

And, cos(A - B) = √3/2

⇒ cos(A - B) = cos30°

⇒ A – B = 30° ….(ii)

Adding (i) and (ii)

We get, 2A = 90°

⇒ A = 45°

Putting in (i)

We get,

⇒ 45° + B = 60°

⇒ B = 15°

∴ A and B are 45°and 15°

Short trick

sin(A + B )= sin60

cos(A - B) = cos30°

So, A + B = 60° and A – B = 30°

Takes oprtion he different is 30° and sum is 60°

So option B and D are satisfy but in option D difference is negative

Then option B is right

A= 45° and B = 15°