If sin θ = $\dfrac{24}{25}$, find the value of cosec θ + cot θ

The correct answer is $\dfrac{4}{3}$

In a right angled triangle, sin θ = $\frac{Perpendicular}{Hypotenuse}$ = $\dfrac{24}{25}$
Using Pythagoras Theorem, (Base)² = √(25² - 24²) = 49
∴ Base = 7

cosec θ = $\dfrac{Hypotenuse}{Perpendicular}$ = $\dfrac{25}{24}$

cot θ = $\dfrac{Base}{Perpendicular}$ = $\dfrac{7}{24}$

∴ cosec θ + cot θ = $\dfrac{25}{24}$ + $\dfrac{7}{24}$ = $\dfrac{32}{24}$ = $\dfrac{4}{3}$