Question

if cos theta equals to
$\sqrt{21} \div 5$
. find the value of
$10 + 10 \ {cot}^{2} \: theta$
​

Answer 1

Answer:

Step-by-step explanation:

$\cos \theta=\frac {\sqrt{21}}{5}\\\\\\Then \ \sin\theta =\sqrt{1-\cos^2\theta} \\\\=\sqrt{1-\frac{21}{25} }\\\\=\sqrt{\frac{4}{25} }=\frac{2}{5}$

Now

$10+10\cot ^2\theta\\\\=10(1+\cot^2\theta}\\\\=10 \ cosec^2 \ \theta\\\\=\frac{10}{\sin^2\theta}\\\\=\frac{10}{\frac{4}{25}} \\\\=\frac{10\times 25}{4}\\\\=\frac{125}{2}$