-
If α, β and γ each is positive acute angle, and sin (α + β – γ) = 1/2 , cos (β + γ – α) = 1/2 and tan (γ + α – β) = 1 then 2α + β = ?
-
- 105°
- 115°
- 110°
- 120°
- 105°
Correct Option: D
sin(α + β – γ) = 1/2 ,
cos (β + γ– α) = 1/2
and tan(γ + α – β) = 1
⇒ sin (α + β – γ) = sin30°, cos (β + γ– α) = cos60° and tan (γ + α – β) = tan 45°
⇒ α + β – γ = 30° .....(i)
β + γ– α = 60° ......(ii)
γ + α – β = 45° ......(iii)
By equations (i) + (ii) and equations (i) + (iii).
2β = 90° and 2α = 75°
⇒ β = 45° and 2α = 75°
⇒ 2α + β = 75° + 45° = 120°
