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

Question 180775: Find the exact value of cot(75�). PLEASE HELP ME!!!!! I really dont know what to do!!!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given trigonometric expression.

Use the identity

Rewrite 75 as 45+30 (note: 45 and 30 are known angles on the unit circle)

Use the identity

Evaluate to get 1. Evaluate to get (use the unit circle)

Multiply

Combine the fractions.

Divide the inner fractions (by multiplying by the reciprocal of the second inner fraction)

Cancel out like terms.

Simplify

Flip the fraction.

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Answer:

So
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the exact value of cot(75�).
-------
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.
=========================
Cheers,
Stan H.
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