Question

$if \: 13sin \: theta = 5 \: \: \: then \: what \: is \: the \: value \: of \: cosec \: theta$
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Answer 1

Let, theta = angle A

.

Sin theta = 5/13

$BC/AC = 5/13 = K (let).•. BC = 5K , AC = 13K$

Now,

from∆ABC

$AB = √AC^2 - BC^2= √(13K) ^2 - (5K) ^2= √169K^2 - 25K^2= √144K^2= 12K$

again,

$Cos theta = AB/AC = 12K/13K = 12/13$

and,

$Cot theta = AB/BC = 12K/5K = 12/5$