Question

If cos (A + B) = 0 and sin (A - B) = 3, then find the value of A and B where A and B are acute angles.

Answer 1

Answer: A=45°,B = 45°

Step-by-step explanation:

cos(A+B)= cos{90०-(A+B)}

A+B=90°-(A+B)

A+A+ B- B=90°

2A=90°

A=45°

substitute value of A = 45°therefore

B = 45°

HOPE THIS HELPS YOU :)

Answer 2

The values of A = 60° and B = 30°

Given:

cos (A + B) = 0 and sin (A - B) = 1/2

where A and B are acute angles

       

To find:

Find the value of A and B  

Solution:

Complete question:

If cos(A+B) = 0 and sin(A−B) = 1/2, then find the value of A and B where A and B are actual angles.

Formulas used:

Cos 90° = 0 and Sin 30° = 1/2

Acute angles:

An acute angle is one that is smaller than 90 degrees in measure. In other words, angles that are less than a right angle (which is equal to 90°) is known as Acute angle.

Here we have

cos (A + B) = 0 and sin (A - B) = 1/2

Take cos (A + B) = 0  

=> cos (A + B) = Cos 90°     [ ∵ Cos 90° = 0 ]

=> A + B = 90° ----- (1)

Take sin(A−B) = 1/2

=> sin(A−B) = Sin 30°    

=> A − B = 30° ----- (2)

Add (1) and (2)  

=> A + B + A − B = 90° + 30°  

=> 2A = 120°

=> A = 60°  

From (1)

=> 60° + B = 90°

=> B = 30°  

Therefore,

The values of A = 60° and B = 30°

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