Toolkit 36General Solutions of Trigonometric Equationssinα=sinβ ⇒ α=β+360k, 180−β+360k, k∈Z\sin\alpha=\sin\beta\;\Rightarrow\;\alpha=\beta+360k,\;180-\beta+360k,\;k\in\mathbb{Z}sinα=sinβ⇒α=β+360k,180−β+360k,k∈Zcosα=cosβ ⇒ α=±β+360k, k∈Z\cos\alpha=\cos\beta\;\Rightarrow\;\alpha=\pm\beta+360k,\;k\in\mathbb{Z}cosα=cosβ⇒α=±β+360k,k∈Ztanα=tanβ ⇒ α=β+180k, k∈Z\tan\alpha=\tan\beta\;\Rightarrow\;\alpha=\beta+180k,\;k\in\mathbb{Z}tanα=tanβ⇒α=β+180k,k∈Zcotα=cotβ ⇒ α=β+180k, k∈Z\cot\alpha=\cot\beta\;\Rightarrow\;\alpha=\beta+180k,\;k\in\mathbb{Z}cotα=cotβ⇒α=β+180k,k∈ZRelated ProblemsCoreAMC 12A Spring 2021 (Problem 19)AMC 12A Fall 2021 (Problem 19)MinorAMC 12B 2025 (Problem 21)