Question

if sin (A-B)=1/2,cos(A+B)=1/2,find A and B​

Answer 1

Given :

• sin (A-B)=1/2
• cos(A+B)=1/2

To Find :

• A and B

Solution :

★ sin (A-B)=1/2

We know that sin 30° = 1/2

Thus,

sin (A-B) = sin 30°

A-B = 30° ----------> (1)

★ cos(A+B)=1/2

We know that cos 60° = 1/2

Thus,

cos (A+B) =cos 60°

A+B = 60° ----------> (2)

Equations :

• A-B = 30° ----------> (1)
• A+B = 60° ----------> (2)

Adding (1) and (2) equation, we get

A - B = 30

A + B = 60

-----------------

2A = 90

-----------------

⇒ 2A = 90

⇒ A = 90/2

⇒ A = 45°

Putting A = 45° in equation (2)

⇒ A+B = 60°

⇒ 45 + B = 60°

⇒ B = 60 - 45

⇒ B = 15°

•°• Hence, A = 45° and B = 15°

Answer 2

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