Question

if sin(a-b) =1/2,cos (a+b) =1/2,0 <a+b<90,a>b, find a and b.

Answer 1

Sin(a-b)=1/2
Sin(a-b)=sin 30
a-b = 30
Cos (a+b)=1/2
Cos(a+b)=1/2
Cos (a+b)=cos 60 a+b=60
Now solving both eqn
a=45
b=15

Answer 2

sin (a-b) = 1/2
sin (a-b) = sin 30°
=> a-b = 30° ----(1)
And, cos (a+b) = 1/2
cos (a+b) = cos 60°
=> a+b = 60° ----(2)
Now, on adding equation (1) & (2), we get
a = 45° & b = 15°