Монгол Бодлогын Сан

Заавар: $$\begin{align*} \tg\alpha&=\dfrac{\sin\alpha}{\cos\alpha}\\ 1-2\sin^2\alpha&=\cos2\alpha\\ \sin\alpha\cdot\cos\alpha&=\dfrac12\sin2\alpha\\ \tg(180^\circ-\alpha)&=-\tg\alpha\\ \cos(180^\circ-\alpha)&=-\cos\alpha \end{align*}$$

Бодолт: $$\begin{align*} \dfrac{2\sin^270^{\circ}-1}{\tg 115^{\circ}\cdot \cos^2 115^{\circ}}&=\dfrac{-\cos140^\circ}{-\tg 65^\circ\cdot\cos^265^\circ }=\dfrac{\cos 140^{\circ}}{\dfrac{\sin 65^\circ}{\cos65^\circ}\cdot \cos^265^{\circ}}\\ &=\dfrac{\cos140^\circ}{\frac12\sin130^\circ}=\dfrac{2\cos(90^\circ+50^\circ)}{\sin(180^\circ-50^\circ)}=\dfrac{-2\sin50^\circ}{\sin50^\circ}=-2 \end{align*}$$