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

1 Answer
Nov 22, 2017

See explanation.

Explanation:

First I calculate both trigonometric functions:

cos((5pi)/4)=cos(pi+pi/4)=-cos(pi/4)=-sqrt(2)/2

cot((5pi)/3)=cot(2pi-pi/3)=cot(-pi/3)=-cot(pi/3)=

=-sqrt(3)/3

Now if we add voth expressions we get:

-(sqrt(2)/2+sqrt(3)/3)=-((3sqrt(2))/6+(2sqrt(3))/6)=

=(-3sqrt(2)-2sqrt(3))/6