An Acute Triangle Bound

★ 7/10Law of Sines trigonometry Extrema Trigonometric Identities Triangle Geometry

Problem

In an acute triangle $ABC$ , the sides opposite $A, B, C$ are $a, b, c$ . Given

\frac{\sin(A - B)}{\cos B} = \frac{\sin(A - C)}{\cos C}, \qquad a\sin C = 1,

find the maximum value of $\dfrac{1}{a^2} + \dfrac{1}{b^2}$ .

Answer

Solution

Difficulty	7/10
Topics	Law of Sines, trigonometry, Extrema, Trigonometric Identities, Triangle Geometry

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