Question

(sina*ctga/cos^2a)-tga*sina​

Answer 1

$\dfrac{\sin \alpha \cdot \text {ctg} \ \alpha }{\cos ^{2} \alpha} - \text{tg} \ \alpha \cdot \sin \alpha = \dfrac{\sin \alpha \cdot \cos \alpha}{\cos^{2} \alpha \cdot \sin \alpha} - \dfrac{\sin \alpha}{\cos \alpha} \cdot \sin \alpha =\\\\= \dfrac{1}{\cos \alpha} - \dfrac{\sin ^{2} \alpha}{\cos \alpha} = \dfrac{1 - \sin ^{2} \alpha}{\cos \alpha} = \dfrac{\cos ^{2} \alpha}{\cos \alpha} = \cos \alpha$