+0  
 
0
1397
2
avatar

How does one solve tan(75) by using a half -angle identity?

Guest May 13, 2014

Best Answer 

 #1
avatar+92808 
+5

One half-angle identity for the tangent is given by

tan (a/2) = (1 - cos a) / sin a

So....a, in this case, is 150 degrees.   And we have

tan (75) = tan (150/2) = ( 1 - cos 150) / sin (150) = [1 - (-√3/2)] / (1/2) = [1 + √3/2] / (1/2) =

2 [ 2 + √3] / 2 = [ 2 + √3] ≈ 3.732

Note...the same result could have been obtained by using the tangent angle sum identity with the angles 30 degrees and 45 degrees.

CPhill  May 13, 2014
 #1
avatar+92808 
+5
Best Answer

One half-angle identity for the tangent is given by

tan (a/2) = (1 - cos a) / sin a

So....a, in this case, is 150 degrees.   And we have

tan (75) = tan (150/2) = ( 1 - cos 150) / sin (150) = [1 - (-√3/2)] / (1/2) = [1 + √3/2] / (1/2) =

2 [ 2 + √3] / 2 = [ 2 + √3] ≈ 3.732

Note...the same result could have been obtained by using the tangent angle sum identity with the angles 30 degrees and 45 degrees.

CPhill  May 13, 2014
 #2
avatar+94120 
0

I don't remember ever seeing this identity before!  

Thanks Chris.   

Melody  May 13, 2014

10 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.