$\displaystyle dx/(5+4sin x)$
step by step explanation would be appreciated
thanks
The complete substitution is...
$\displaystyle \displaystyle t= \tan \frac{x}{2}$
$\displaystyle \displaystyle dx= \frac{2\ dt}{1+t^{2}}$
$\displaystyle \displaystyle \sin x= \frac{2\ t}{1+t^{2}}$
$\displaystyle \displaystyle \cos x= \frac{1-t^{2}}{1+t^{2}}$
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$
$\displaystyle \displaystyle \sin x = 2 \sin \frac{x}{2}\ \cos \frac{x}{2} = \frac{2 \sin \frac{x}{2}\ \cos \frac{x}{2}}{\sin^{2} \frac{x}{2} + \cos^{2} \frac{x}{2}} = \frac{2\ \tan \frac{x}{2}}{1+\tan^{2} \frac{x}{2}} = \frac{2 t}{1+t^{2}}$
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$