Hi All,
I'm new to this blessed site.
Would appreciate someone's help in simplifying the following equation:
Many thanks !
$\displaystyle \frac{\tan(x) \sin(x)}{\sec^2(x) - 1} = \frac{\tan(x) \sin(x)}{1 + \tan^2(x) - 1} = \frac{\tan(x) \sin(x)}{\tan^2(x)} = \frac{\sin(x)}{\tan(x)}$.
And $\displaystyle \tan(x) = \frac{\sin(x)}{\cos(x)}$ so we have...
$\displaystyle \frac{\sin(x)}{\tan(x)} = \frac{\sin(x)}{\frac{\sin(x)}{\cos(x)}} = \cos(x)$.
If you need clarification on the last step then...
$\displaystyle \frac{\cos(x)}{\cos(x)} = 1$ so...
$\displaystyle \frac{\sin(x)}{\frac{\sin(x)}{\cos(x)}} \cdot 1 = \frac{\sin(x)}{\frac{\sin(x)}{\cos(x)}} \cdot \frac{\cos(x)}{\cos(x)} =$ $\displaystyle \frac{\sin(x)\cos(x)}{\frac{\sin(x)\cos(x)}{\cos(x )}} = \frac{\sin(x) \cos(x)}{\sin(x)} = \cos(x)$