Question

If 2 cos (A + B) = 2 sin (A - B) = 1; find
the values of A and B.

Answer 1

Answer:

2cos(A+B)=1

cos(A+B)=

2

1

cos(A+B)=cos60

∘

A+B=60

∘

........ (1)

2sin(A−B)=1

sin(A−B)=

2

1

sin(A−B)=sin30

∘

A−B=30

∘

........ (2)

Adding (1) and (2),

2A=90

∘

A=45

∘

From (1),

B=60

∘

−A

=60

∘

−45

∘

=15

∘