We have, a‌cos‌θ+b‌sin‌θ=c .......(i) ∵α and β(α≠β) satisfy the Eq. (i) ⇒a‌cos‌α+b‌sin‌α=c .........(i) and a‌cos‌β+b‌sin‌β=c......... (iii) Now, subtracting Eq. (iii) from Eq. (ii), we get a‌cos‌α+b‌sin‌α−a‌cos‌β−b‌sin‌β=0 ⇒a(cos‌α−cos‌β)+b(sin‌α−sin‌β)=0 ⇒a(cos‌α−cos‌β)=−b(sin‌α−sin‌β) ⇒a‌sin‌