Show that ( 3A - A)/( 3A + A) = 2A

April 13, 2026Mathematics

ScanSolve AI Answer

April 13, 2026

Answer

\tan 2A$.

Hey Dany — ready when you are.

3. (i) Self-correction: The problem asks to show that $\frac{\sin 3A - \sin A}{\cos 3A + \cos A} = \tan 2A$ . Using sum-to-product identities: $\sin X - \sin Y = 2 \cos \left(\frac{X+Y}{2}\right) \sin \left(\frac{X-Y}{2}\right)$ $\cos X + \cos Y = 2 \cos \left(\frac{X+Y}{2}\right) \cos \left(\frac{X-Y}{2}\right)$

Let $X = 3A$ and $Y = A$ .

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Asked on April 13, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 13, 2026

Hey Dany — ready when you are. 3. (i) Self-correction: The problem asks to show that ( 3A - A)/( 3A + A) = 2A. Using sum-to-product identities: X - Y = 2 ((X+Y)/(2)) ((X-Y)/(2)) X + Y = 2 ((X+Y)/(2)) ((X-Y)/(2)) Let X = 3A and Y = A.