Question

Calculate
$\frac{\sin \alpha }{{\sin }^3\alpha +{\cos }^3\alpha }$ if $\tan$ $\alpha$ =2.

Answer 1

For such kind of question we have to just simplify the question as much possible, so first we take common $(\cos \alpha {)}^3$ from denominator and then we got

$\frac{\tan \alpha \times (\sec \alpha {)}^2}{1+(\tan \alpha {)}^3}$

and using trignometric relation we convert sec into tan after that

$\frac{\tan \alpha \times (1+{\left(\tan \alpha \right)}^2)}{1+(\tan \alpha {)}^3}$

and as given the value of $\tan \alpha$ put this and solve simple calculation we got the value of expression is equal to $\frac{10}{9}$