Question

If sin (A+B) =ROOT 3 /2and tan A=1 then find angle B​

Answer 1

Answer:

$\pi /12$ (15°)

Step-by-step explanation:

sin (A+B) = $\sqrt{3}/2$

⇒ sin (A+B) = sin 60°          [∵ sin 60° = $\sqrt{3}/2$]

⇒ A+B = 60° = π/3

given

tan A = 1

⇒ tan A = tan 45°         [∵ tan 45° = 1]

∴ A = 45°

∴ A+B = 60°

⇒45° + B = 60°

∴ B = 60° - 45° = 15° = $\pi /12$