Question

Express the following in terms of trigonometric ratios of angles lying between 0 and 45:
$\text{cosec}{54}^0+\sin {72}^0$

Answer 1

We have,

$\csc ({90}^0-\theta )=\sec \theta$ and $\sin ({90}^0-\theta )=\cos \theta$

$\csc {54}^0=\csc ({90}^0-{36}^0)=\sec {36}^0$

$\sin {72}^0=\sin ({90}^0-{18}^0)=\cos {18}^0$

$\therefore \csc {54}^0+\sin {72}^0=\sec {36}^0+\cos {18}^0$