Question

If sin (A+B) = 1 and cos (A$-$B) = $\frac{\sqrt{3}}{2}$ find the value of A and B.

Answer 1

Given:
sin (A + B) = 1 and cos (A − B) = $\frac{\sqrt{3}}{2}$
Consider sin (A + B) = 1
$\Rightarrow$ sin (A + B) = sin 90^o (From the table)
$\Rightarrow$ A + B = 90$°$ … (1)
Now, consider cos (A $-$ B) = $\frac{\sqrt{3}}{2}$
$\Rightarrow$ cos (A − B) = cos 30$°$ (From table)
$\Rightarrow$ A $-$ B = 30$°$ … (2)
Adding the equations (1) and (2), we get:
A + B + A $-$ B = 90$°$ + 30$°$
$\Rightarrow$ 2A = 120$°$
$\Rightarrow$ A = 60$°$
Substituting the value of A in equation (1), we get:
$\Rightarrow$ 60$°$ + B = 90$°$
$\Rightarrow$ B = 90$°$ $-$ 60$°$
$\Rightarrow$B = 30$°$