(sin130^circ cdot cos20^circ )/(cos160^circ )cdot sin50^(circ ) . Madesi

To solve this trigonometric expression, we can use the following identities:<br /><br />1. $\sin(180^\circ - \theta) = \sin(\theta)$<br />2. $\cos(180^\circ - \theta) = -\cos(\theta)$<br /><br />Using these identities, we can rewrite the expression as:<br /><br />$\frac{\sin(130^\circ) \cdot \cos(20^\circ)}{\cos(160^\circ) \cdot \sin(50^\circ)} = \frac{\sin(50^\circ) \cdot \cos(20^\circ)}{-\cos(20^\circ) \cdot \sin(50^\circ)}$<br /><br />Now, we can cancel out the common terms in the numerator and denominator:<br /><br />$\frac{\sin(50^\circ) \cdot \cos(20^\circ)}{-\cos(20^\circ) \cdot \sin(50^\circ)} = -1$<br /><br />Therefore, the correct answer is -1.