Question

if cos(A+B)=½=sin(A-B) find A and B​

Answer 1

Answer:

A = 45° and B = 15°

Step-by-step explanation:

   cos( A + B ) = 1 / 2

 ⇒ cos( A + B ) = cos60°

 ⇒ A + B = 60°            ...( 1 )

   sin( A - B ) = 1 / 2

 ⇒ sin( A - B ) = 1 / 2

 ⇒ sin( A - B ) = sin30°

 ⇒ A - B = 30°           ...( 2 )

 

Adding ( 1 ) and ( 2 ):

⇒ A + B + A - B = 60° + 30°

⇒ 2A = 90°

⇒ A = 45°

     Hence, A - B = 30°

                 45° - B = 30°

                    15° = B

Answer 2

A=45 AND B=15.

refer the pic for the process...

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