Forced by an Identity

★ 7/10Law of Sines trigonometry Law of Cosines AM-GM Triangle Geometry

Problem

In $\triangle ABC$ ,

3\sin^2 B + 7\sin^2 C = 2\sin A\sin B\sin C + 2\sin^2 A.

Find $\sin\left(A + \dfrac{\pi}{4}\right)$ .

Answer

Solution

Difficulty	7/10
Topics	Law of Sines, trigonometry, Law of Cosines, AM-GM, Triangle Geometry

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