How do I find the exact value of $cos (\frac{5 π}{4}) + cot (\frac{5 π}{3})$ $cos ((5pi)/4)+cot((5pi)/3)$ ?

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How do I find the exact value of $cos (\frac{5 π}{4}) + cot (\frac{5 π}{3})$ $cos ((5pi)/4)+cot((5pi)/3)$ ?

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Answer 1 · 2017-11-22T10:15:55

See explanation.

Explanation:

First I calculate both trigonometric functions:

$cos (\frac{5 π}{4}) = cos (π + \frac{π}{4}) = - cos (\frac{π}{4}) = - \frac{\sqrt{2}}{2}$ $cos((5pi)/4)=cos(pi+pi/4)=-cos(pi/4)=-sqrt(2)/2$

$cot (\frac{5 π}{3}) = cot (2 π - \frac{π}{3}) = cot (- \frac{π}{3}) = - cot (\frac{π}{3}) =$ $cot((5pi)/3)=cot(2pi-pi/3)=cot(-pi/3)=-cot(pi/3)=$

$= - \frac{\sqrt{3}}{3}$ $=-sqrt(3)/3$

Now if we add voth expressions we get:

$- (\frac{\sqrt{2}}{2} + \frac{\sqrt{3}}{3}) = - (\frac{3 \sqrt{2}}{6} + \frac{2 \sqrt{3}}{6}) =$ $-(sqrt(2)/2+sqrt(3)/3)=-((3sqrt(2))/6+(2sqrt(3))/6)=$

$= \frac{- 3 \sqrt{2} - 2 \sqrt{3}}{6}$ $=(-3sqrt(2)-2sqrt(3))/6$

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How do I find the exact value of $cos (\frac{5 π}{4}) + cot (\frac{5 π}{3})$ $cos ((5pi)/4)+cot((5pi)/3)$ ?

1 Answer

Explanation:

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