SOLUTION: Please help me solve this equation for an exact value: This is where I am so far, but I am stuck on where to go next and am not sure if I have done it properly to this point.

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me solve this equation for an exact value: This is where I am so far, but I am stuck on where to go next and am not sure if I have done it properly to this point.       Log On


   

Question 424118: Please help me solve this equation for an exact value:
This is where I am so far, but I am stuck on where to go next and am not sure if I have done it properly to this point.


tan(cos-1(1/2)-sin-1(3/4))

tan(α-β)=(tan α - tan β) / (1 + tan α * tan β)

tan (√3-(3/√7)) = (√3-(3/√7))/(1+(√3*(3/√7)))



Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!



Write that as



Multiply that by sqrt%287%29%2Fsqrt%287%29 written as

%28sqrt%287%29%2F1%29%2F%28sqrt%287%29%2F1%29




Distribute and get:

%0D%0A%0D%0A%28sqrt%2821%29-3%29%2F%28sqrt%287%29%2B3sqrt%283%29%29+

Rationalize the denominator by multiplying by

%28sqrt%287%29-3sqrt%283%29%29%2F%28sqrt%287%29-3sqrt%283%29%29














%2816sqrt%283%29-12sqrt%287%29%29%2F%28-20%29

Reverse the terms on the top

%28-12sqrt%287%29%2B16sqrt%283%29%29%2F%28-20%29

Factor -4 out of the top:

%28-4%283sqrt%287%29-4sqrt%283%29%29%29%2F%28-20%29

The -4 cancels into the -20 giving 5 on the bottom:

%283sqrt%287%29-4sqrt%283%29%29%2F5

Edwin