# If sin(A-B)=1/2,cos(A+B)=1/2,0≤A+B≤90,A>B,THEN FIND THE VALUE OF A?

2
by prabhushettisan

2014-10-19T00:31:31+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Cos(A+B) = 1/2
⇒cos (A+B) = cos(60)  (as 0<A+B<90)
⇒A+B = 60

sin(A-B) = 1/2
⇒sin(A-B) = sin(30) or sin (150)
⇒A-B = 30 or 150

Case:1
A - B = 30
A + B = 60
Solving we get, A = 45 and B = 15
A>B is satisfied.

Case:2
A - B = 150
A + B = 60
Solving, we get A = 105, B = -45
A>B is satisfied.

So the value of A can be 45 or 105.
i didnt understand
you need to convert 1/2 into cos(x) or sin(x) as needed..
2014-10-19T06:21:20+05:30
Sin(A-B) =1/2
sin(A-B) =sin 30       (bcause 1/2=30)
A-B=30---------------------1
cos(A+B) = 1/2
cos (A+B) =cos 60
A+B = 60-------------------2
Adding 1 and 2 we get 2A = 90
A = 90/2
A= 45
substituting A=45 in 1
A-B = 30
45-B=30
-B=30-45
-B=-15
B=15

Thank you amina