Solution:
We have been given that πππ 2π΄ = π ππ (π΄ β 15Β°) and we need to find the value of β π΄.
We know that, for any angle ΞΈ,
π ππ (90Β° β ΞΈ) = πππ ΞΈ
Therefore we can say that, πππ 2π΄ = π ππ (90Β° β 2π΄)
Since, πππ 2π΄ = π ππ (π΄ β 15Β°)
βπ ππ (90Β° β 2π΄) = π ππ (π΄ β 15Β°)
β 90Β°β2π΄ = π΄ β 15Β°
β π΄ = 35Β°
Hence, the angle π΄ is equal to 35Β°.
