Question

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

Answer 1

Answer:

sin(a-b) = 1/2

sin(a-b) = sin 30 degree

a-b = 30---------1st equation

cos(a+b) = 1/2

cos(a+b) = cos 60 degree

a+b = 60--------2nd equation

solve 1 and 2

a-b+a+b = 90

2a = 90

a=45

substitute in 2nd equation

a+b = 60

b=60-45

b = 15

=> a=45 b=15