Question

if Cos( A-b) is equal to ✓ 3\2 and sin( a + b )= 1 then find the value of a and b

Answer 1

cos( a - b ) = $\dfrac{\sqrt{3}}{2}$

cos( a - b ) = cos30°

       a - b = 30°            -------: ( 1 )

sin( a + b ) = 1

sin( a + b ) = sin 90°

      a + b = 90°        --------: ( 2 )

       

            Adding ( 1 ) & ( 2 )

a - b = 30°

a + b = 90°

________

2a = 120°

________

a = $\dfrac{120°}{2}$

a = 60°

          Substituting the value of a in ( 1 )

a - b = 30°

60° - b = 30°

60° - 30° = b

30° = b

Therefore, value of a = 60°

                   value of b = 30°

Answer 2

$\cos(a - b) = \frac{ \sqrt{3} }{2} \\ \cos(a - b) = \cos(30) \\ \\ so \\ \: \: \: \: \:a - b = 30 \: \: \: \: \: .........(1) \\ \\ \\ \sin(a + b) = 1 \\ \sin(a + b) = \sin(90) \\ \\ so \\ \: \: \: \: \: a + b = 90 \: \: \: \: \: .........(2)$


equation (1)+ equation (2)
$a - b = 30 \\ a + b = 90$
____________
$2a = 120 \\ a = \frac{120}{2} \\ a = 60$


substituting the value of a in equation (1)


$60 - b = 30 \\ 60 - 30 = b \\ b = 30$



So the value of a is 60 and b is 30.