Question

Find $a$ if$\frac{\cos ({90}^{\circ }+\theta )\sec (-\theta )\tan ({180}^{\circ }-\theta )}{\sec ({360}^{\circ }-\theta )\sin ({180}^{\circ }+\theta )\cot ({90}^{\circ }-\theta )}=-a$

Answer 1

consider, L.H.S $=\frac{\cos ({90}^{\circ }+\theta )\sec (-\theta )\tan ({180}^{\circ }-\theta )}{\sec ({360}^{\circ }-\theta )\sin ({180}^{\circ }+\theta )\cot ({90}^{\circ }-\theta )}$

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

$=-1=-a$
$\therefore a=1$