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

April 14, 2026Mathematics

ScanSolve AI Answer

Answer

6.5

4 steps

Применим формулу синуса двойного угла $\sin(2\alpha) = 2 \sin \alpha \cos \alpha$ .
$\frac{13 \sin 26^\circ \cos 26^\circ}{\sin 52^\circ} = \frac{13}{2} \cdot \frac{2 \sin 26^\circ \cos 26^\circ}{\sin 52^\circ}$
Заменим $2 \sin 26^\circ \cos 26^\circ$ на $\sin(2 \cdot 26^\circ)$ .
$\frac{13}{2} \cdot \frac{\sin(2 \cdot 26^\circ)}{\sin 52^\circ} = \frac{13}{2} \cdot \frac{\sin 52^\circ}{\sin 52^\circ}$
Сократим $\sin 52^\circ$ .
$\frac{13}{2} \cdot 1 = \frac{13}{2}$
Вычислим значение.
$\frac{13}{2} = 6.5$ $6.5$

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