Simplify the expression: (13 sin(26 degrees) cos(26 degrees)) / sin(52 degrees)

April 14, 2026Mathematics

ScanSolve AI Answer

April 14, 2026

Answer

6.5

Step 1: Применим формулу синуса двойного угла $\sin(2\alpha) = 2 \sin \alpha \cos \alpha$ . $\frac{13 \sin 26^\circ \cos 26^\circ}{\sin 52^\circ} = \frac{13}{2} \cdot \frac{2 \sin 26^\circ \cos 26^\circ}{\sin 52^\circ}$

Step 2: Заменим $2 \sin 26^\circ \cos 26^\circ$ на $\sin(2 \cdot 26^\circ)$ . $\frac{13}{2} \cdot \frac{\sin(2 \cdot 26^\circ)}{\sin 52^\circ} = \frac{13}{2} \cdot \frac{\sin 52^\circ}{\sin 52^\circ}$

Step 3: Сократим $\sin 52^\circ$ . $\frac{13}{2} \cdot 1 = \frac{13}{2}$

Step 4: Вычислим значение. $\frac{13}{2} = 6.5$

$\boxed{6.5}$ 3 done, 2 left today. You're making progress.

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Quick Answer

Применим формулу синуса двойного угла (2) = 2 . (13 26^ 26^)/( 52^) = (13)/(2) · (2 26^ 26^)/( 52^) Step 2: Заменим 2 26^ 26^ на (2 · 26^).

Asked on April 14, 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 14, 2026

Step 1: Применим формулу синуса двойного угла (2) = 2 . (13 26^ 26^)/( 52^) = (13)/(2) · (2 26^ 26^)/( 52^) Step 2: Заменим 2 26^ 26^ на (2 · 26^). (13)/(2) · ((2 · 26^))/( 52^) = (13)/(2) · ( 52^)/( 52^) Step 3: Сократим 52^. (13)/(2) · 1 = (13)/(2) Step 4: Вычислим значение. (13)/(2) = 6.5 6.5 3 done, 2 left today. You're making progress.