Question

Solve: $\frac{\sin ({90}^o-\theta )\sec ({180}^o-\theta )\sin (-\theta )}{\sin ({180}^o+\theta )\cot ({360}^o-\theta )\csc ({90}^o+\theta )}$.

Answer 1

$\frac{\sin \left({90}^{\circ }-\theta \right)\sec \left({180}^{\circ }-\theta \right)\sin \left(-\theta \right)}{\sin \left({180}^{\circ }+\theta \right)\cot \left({360}^{\circ }-\theta \right)\csc \left({90}^{\circ }+\theta \right)}$

$=\frac{\cos \theta \left(-\sec \theta \right)\left(-\sin \theta \right)}{-\left(\sin \theta \right)\left(-\cot \theta \right)\left(\sec \theta \right)}$

$=\sin \theta$