Монгол Бодлогын Сан

Заавар:\begin{gather} \sin2\alpha=2\sin\alpha\cos\alpha\\ \sin\left(\frac{\pi}{2}-\alpha\right)=\cos\alpha\\ \cos\left(\frac{\pi}{2}-\alpha\right)=\sin\alpha \end{gather}

Бодолт:\begin{align*} \text{Илэрх.}&=\dfrac{\sin 2t -2\sin (\frac{\pi}{2}-t)}{\cos(\frac{\pi}{2}-t)-\sin^2t}\\ &=\dfrac{2\sin t\cos t-2\cos t}{\sin t-\sin^2t}\\ &=\dfrac{2\cos t(\sin t-1)}{\sin t(1-\sin t)}\\ &=-\dfrac{2\cos t}{\sin t}\\ &=-2\ctg t \end{align*}