Question

cos(A+B)=1/2=SIN(A-B)

Answer 1

Answer:

Value of A is 45° and value of B is 15°

Step-by-step explanation:

Given,

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

Then,

⇒ cos( A + B ) = 1 / 2

From trigonometric table, we know that the value of 1 / 2 is cos60° or sin30°.

So,

⇒ cos( A + B ) = cos60°

⇒ A + B = 60°             ...( 1 )

And, sin( A - B ) = 1 / 2

⇒ sin( A - B ) = sin30°

⇒ A - B = 30               ...( 2 )

Now, adding ( 1 ) and ( 2 ),

A + B = 60°

A - B = 30°

2A    = 90°

A = 90° / 2

A = 45°

Substituting the value of A in ( 1 ),

= >  A + B = 60°

= >  45° + B = 90°

= >  B = 60° - 45°

= >  B = 15°

Therefore the value of A is 45° and value of B is 15°