Question

If x = sin (${90}^{\circ }$- a) cot (${90}^{\circ }$- a), then x is equal to ............................

Answer 1

cot(90 - a) = $\frac{cos({90}^{\circ }-a)}{sin({90}^{\circ }-a)}$

Hence sin $({90}^{\circ }-a)$ cot $({90}^{\circ }-a)$ = sin$({90}^{\circ }-a)$ $\times$ $\frac{cos({90}^{\circ }-a)}{sin({90}^{\circ }-a)}$

= cos$({90}^{\circ }-a)$

=sin a.