Question

If cosec^2θ = 25 16 then find the value of sinθ.

Answer 1

$\large \tt cosec \: 2 \theta = \frac{25}{16} = \frac{25}{16} \\ \\ \large \tt cosec \theta \: = \frac{1}{ \: cos \theta \: } \: = > cos \theta = \frac{1}{cosec \theta} \\ \\ \\ \large \tt cos \theta \: = \frac{16}{25} = \frac{base \: \: of \: \triangle}{ \: \: hypotonuse \: \: of \: \triangle \: \: } \\ \\ \\ \large \tt sin \theta = \frac{height \: \: of \: \triangle}{hypotonuse} \\ \\ \\ \\ \large \tt by \: \: pythagorous \: \: theorem \: \: \\ \\ \\ \large \tt {(height(h))}^{2} = {(hypo)}^{2} - {(base)}^{2} \\ \\ \\ \large \tt {(h)}^{2} = {(25)}^{2} - {(16)}^{2} = 625 - 256 = 369 \\ \\ \\ \large \tt h = \sqrt{369} = 19$

$\huge \color{darkcyan}\tt sin \theta = \frac{19}{25}$