Question

Show that $\frac{\sqrt{(cose{c}^2\Theta -1)}}{cosec\Theta }=cos\Theta$

Answer 1

$Si{n}^2\theta +co{s}^2\theta =1$

$1+co{t}^2\theta cose{c}^2\theta$ (dividing by $si{n}^2\theta$)

$co{t}^2\theta =cose{c}^2\theta -1$

So, $\frac{\sqrt{(cose{c}^2\theta -1)}}{cosec\theta }=cot\theta \times sin\theta =cos\theta$