If tan (A-B)=1 and sin (A+B)=(√3/2), then find B.

Question

If tan (A-B)=1 and sin (A+B)=(√3/2), then find B. (A) 42 (1°/2) (B) 7 (10°/2) (C) 15 (1°/2) (D) 60°

Tardigrade Admin · Accepted Answer

(i) Use tan 45°=1 and sin 60°=(√3/2). (ii) If tan (A-B)=1, then A-B=45°. (iii) If sin (A+B)=(√3/2), then A+B=60°. (iv) Subtract the above two equations and find B.

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

$42 \frac{1 ^{\circ}}{2}$

$7 \frac{1 0 ^{\circ}}{2}$

$15 \frac{1 ^{\circ}}{2}$

$6 0^{\circ}$

(i) Use $tan 4 5^{\circ} = 1$ and $sin 6 0^{\circ} = \frac{3}{2}$ .
(ii) If $tan (A - B) = 1$ , then $A - B = 4 5^{\circ}$ .
(iii) If $sin (A + B) = \frac{3}{2}$ , then $A + B = 6 0^{\circ}$ .
(iv) Subtract the above two equations and find B.

Q. If tan(A−B)=1 and sin(A+B)=23​​, then find B.

4221∘​

7210∘​

1521∘​

60∘