Question

If sin (a-b)=1/2 cos (a+b)=1/2, 0 degree b find a and b

Answer 1

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 )

         Adding ( 1 ) &  ( 2 ) ,

a - b = 30°

a + b = 60°

_________

2a = 90°

_________

a = $\dfrac{90 \degree}{2}$

a = 45°

     Substituting the value of in ( 1 )

a - b = 30°

45° - b = 30°

45° - 30° = b

15° = b

Therefore, a = 45° and b = 15°

Answer 2

$\huge \bold {\mathfrak {hey}}$

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

To find = value of "a" and "b"


Now,

sin ( a - b) = 1/2

sin ( a - b) = sin 30°

Therefore,

➡️ a - b = 30° - - - - - - - - (1)

Now,

cos (a +b) =1/2
cos ( a+b) = cos 60°
a + b = 60° - - - - - - - - - (2)


Now,

Adding equation (1) and (2)

➡️ a-b = 30°
➡️ a +b = 60°

➡️ 2a = 90°

➡️ a = 45°

Now in equation substitute

➡️ a-b = 30
➡️ 45 - b = 30
➡️ b = 15

++++++++++++++++++++++++++

$\huge \boxed { a = 45°}$

$\huge \boxed { b = 15°}$

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