Question

Evaluate:$\mathrm{cosec}31°–\sec 59°$

Answer 1

To simplify this, convert the cosec function into $\sec$ function

$31°$ is written as

$31°=90°–59°$

$\mathrm{cosec}31°=\mathrm{Cosec}(90°-59°)$ $[\mathrm{cosec}(90°-\mathrm{\theta })=\mathrm{Sec}\mathrm{\theta }]$

$\mathrm{cosec}(90°-59°)=\mathrm{Sec}59°$

Substitute the value, to simplify this equation, we get

$\mathrm{cosec}31°–\sec 59°=\mathrm{Sec}59°–\sec 59°$

$\mathrm{cosec}31°–\sec 59°=0$