Question

If $\tan (A-B)=1$ and $\sin (A+B)=\frac{\sqrt{3}}{2}$, then find $B$.

• A. $42 \frac{1^{\circ}}{2}$
• B. $7 \frac{10^{\circ}}{2}$
• C. $15 \frac{1^{\circ}}{2}$
• D. $60^{\circ}$

Answer 1

Answer: (B)

(i) Use $\tan 45^{\circ}=1$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$.
(ii) If $\tan (A-B)=1$, then $A-B=45^{\circ}$.
(iii) If $\sin (A+B)=\frac{\sqrt{3}}{2}$, then $A+B=60^{\circ}$.
(iv) Subtract the above two equations and find B.