Question

find a and b if sin(a-b) =cos(a+b)=½

Answer 1

Hola there,

Given => sin(a - b) = cos(a + b) = 1/2

=> sin(a - b) = cos(a + b)

=> cos(90° - (a - b)) = cos(a + b)

=> 90° - a + b = a + b

=> 2a = 90°

=> a = 45°

Cos(a + b) = 1/2

cos60° = 1/2

So,

=> a + b = 60°

=> 45° + b = 60°

=> b = 60° - 45°

=> b = 15°

Hope this helps...:)

Answer 2

Hi,

Sin(a - b ) = 1/2

sin ( a - b ) = sin 30°

a - b = 30° -----( 1 )

cos ( a + b ) = 1/2

cos ( a + b ) = cos 60°

a + b = 60° ----( 2 )

Add equations ( 1 ) and ( 2 ) , we get

2a = 90

a = 90/2

a = 45°

Put a = 45° in equation ( 2 ) , we get

45 + b = 60

b = 60 - 45

b = 15°

Therefore ,

a = 45° ,

b = 15°

I hope this helps you.

: )