if cos theta equals to
[tex] \sqrt{21} \div 5[/tex]
. find the value of
[tex]10 + 10 \ {cot}^{2} \: theta[/te

if cos theta equals to
[tex] \sqrt{21} \div 5[/tex]
. find the value of
[tex]10 + 10 \ {cot}^{2} \: theta[/tex]

1 thought on “if cos theta equals to <br />[tex] \sqrt{21} \div 5[/tex]<br />. find the value of <br />[tex]10 + 10 \ {cot}^{2} \: theta[/te”

  1. Answer:

    Step-by-step explanation:

    [tex]\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} \\[/tex]

    Now

    [tex]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}[/tex]

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