How do you solve and find the value of $cos (arctan (\frac{3}{5}))$ $cos(arctan(3/5))$ ?

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How do you solve and find the value of $cos (arctan (\frac{3}{5}))$ $cos(arctan(3/5))$ ?

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Answer 1 · 2016-12-23T04:30:14

$cos (arctan (\frac{3}{5})) = \frac{5}{\sqrt{34}}$ $cos(arctan(3/5))=5/sqrt34$

Explanation:

Let $arctan (\frac{3}{5}) = θ$ $arctan(3/5)=theta$

Hence $tan θ = \frac{3}{5}$ $tantheta=3/5$

and $cos (arctan (\frac{3}{5})) = cos θ$ $cos(arctan(3/5))=costheta$

= $\frac{1}{sec θ}$ $1/sectheta$

= $\frac{1}{\sqrt{{sec}^{2} θ}}$ $1/sqrt(sec^2theta)$

= $\frac{1}{\sqrt{1 + {tan}^{2} θ}}$ $1/sqrt(1+tan^2theta)$

= $\frac{1}{\sqrt{1 + {(\frac{3}{5})}^{2}}}$ $1/sqrt(1+(3/5)^2)$

= $\frac{1}{\sqrt{1 + \frac{9}{25}}}$ $1/sqrt(1+9/25)$

= $\frac{1}{\sqrt{\frac{34}{25}}}$ $1/sqrt(34/25)$

= $\sqrt{\frac{25}{34}}$ $sqrt(25/34)$

= $\frac{5}{\sqrt{34}}$ $5/sqrt34$

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How do you solve and find the value of $cos (arctan (\frac{3}{5}))$ $cos(arctan(3/5))$ ?

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How do you solve and find the value of $cos (arctan (\frac{3}{5}))$ $cos(arctan(3/5))$ ?