SOLUTION: Find the exact value of cot(75º). PLEASE HELP ME!!!!! I really dont know what to do!!!

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Question 180775: Find the exact value of cot(75º). PLEASE HELP ME!!!!! I really dont know what to do!!!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
cot%2875%29 Start with the given trigonometric expression.


1%2Ftan%2875%29 Use the identity cot%28A%29=1%2Ftan%28A%29


1%2Ftan%2845%2B30%29 Rewrite 75 as 45+30 (note: 45 and 30 are known angles on the unit circle)


1%2F%28%28tan%2845%29%2Btan%2830%29%29%2F%281-tan%2845%29tan%2830%29%29%29 Use the identity tan%28A%2BB%29=%28tan%28A%29%2Btan%28B%29%29%2F%281-tan%28A%29tan%28B%29%29


1%2F%28%281%2Bsqrt%283%29%2F3%29%2F%281-%281%29%28sqrt%283%29%2F3%29%29%29 Evaluate tan%2845%29 to get 1. Evaluate tan%2830%29 to get sqrt%283%29%2F3 (use the unit circle)


1%2F%28%281%2Bsqrt%283%29%2F3%29%2F%281-sqrt%283%29%2F3%29%29 Multiply


1%2F%28%28%283%2Bsqrt%283%29%29%2F3%29%2F%28%283-sqrt%283%29%29%2F3%29%29 Combine the fractions.


1%2F%28%28%283%2Bsqrt%283%29%29%2F3%29%2A%283%2F%283-sqrt%283%29%29%29%29 Divide the inner fractions (by multiplying by the reciprocal of the second inner fraction)


1%2F%28%28%283%2Bsqrt%283%29%29%2Fcross%283%29%29%2A%28cross%283%29%2F%283-sqrt%283%29%29%29%29 Cancel out like terms.


1%2F%28%283%2Bsqrt%283%29%29%2F%283-sqrt%283%29%29%29 Simplify


%283-sqrt%283%29%29%2F%283%2Bsqrt%283%29%29 Flip the fraction.


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Answer:


So cot%2875%29=%283-sqrt%283%29%29%2F%283%2Bsqrt%283%29%29

Answer by stanbon(48558) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of cot(75º).
-------
cot(x+y) = [cot(x)cot(y)-1] / [cot(x) + cot(y)]
Your Problem:
cot(30 + 45) = [cot(30)cot(45)-1] / [cot(30) + cot(45)]
= [sqrt(3)*sqrt(2)/2 - 1] / [sqrt(3) + sqrt(2)/2]
= [(sqrt(3)*sqrt(2) - 2)/2] / [(2sqrt(3) = sqrt(2))/2]
= etc.
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Cheers,
Stan H.