Question

If Sin(A+B) =V3/2=Cos (A-B),
0°<A+B<90° (A>B),
Find the value of A and B.​

Answer 1

$\bold\red{\fbox{\sf{Solution}}}$

sin(A+B)=cos(A-B)=√3/2

∴, sin(A+B)=√3/2

or, sin(A+B)=sin60°

or, A+B=60° --(1)

cos(A-B)=√3/2

or, cos(A-B)=cos30°

or, A-B=30° --(2)

Adding (1) and (2) we get,

2A=90°

or, A=45°

Putting in (1) we get, 

45°+B=60°

or, B=15°

∴, A=45°, B=15°