Question

if cos(A-B)= 1/2, sin (A+B) = 1/2, find the smallest positive values of A and B and also their most general values​

Answer 1

hope it will help u...

Answer 2

Answer :-

→ A = 105 and B = 45 .

Step-by-step explanation :-

We have,

→ cos( A - B ) = ½ .

→ cos( A - B ) = cos 60° or cos 240°



And,

→ sin( A + B ) = ½ .

→ sin( A + B ) = sin 30° or sin 150°

Since A-B < A+B,

→ cos (A-B) = cos 60°.

→ (A-B) = 60°. --1)

→ sin (A+B) = sin 150°.

→ (A+B) = 150°. --2)




Substracting in equation (1) and (2), we get

A - B = 60 .

A + B = 150

- - -

____________

==> - 2B = -90° .

==> B = 45° .

•°• B = 45°,

Putting the value of B in equation (1), we get

==> A - ( 45) = 60 .

==> A = 60 + 15 .

•°• A = 105°

Hence, it is solved .