How do I find the exact value of cos ((5pi)/4)+cot((5pi)/3)cos(5π4)+cot(5π3)?

1 Answer
Daniel L.
Nov 22, 2017

See explanation.

Explanation:

First I calculate both trigonometric functions:

cos((5pi)/4)=cos(pi+pi/4)=-cos(pi/4)=-sqrt(2)/2cos(5π4)=cos(π+π4)=−cos(π4)=−√22

cot((5pi)/3)=cot(2pi-pi/3)=cot(-pi/3)=-cot(pi/3)=cot(5π3)=cot(2π−π3)=cot(−π3)=−cot(π3)=

=-sqrt(3)/3=−√33

Now if we add voth expressions we get:

-(sqrt(2)/2+sqrt(3)/3)=-((3sqrt(2))/6+(2sqrt(3))/6)=−(√22+√33)=−(3√26+2√36)=

=(-3sqrt(2)-2sqrt(3))/6=−3√2−2√36

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