How do you evaluate arctan((arctan(9/7) - arctan(7/6)) / (arctan(5/3) - arctan(3/2)))?
1 Answer
Apr 1, 2016
Explanation:
Let's rewrite the expression as
epsilon=arctan(theta/rho)
with
theta=arctan(9/7)-arctan(7/6) =>tan theta=tan(arctan(9/7)-arctan(7/6))
rho=arctan(5/3)-arctan(3/2) =>tan rho=tan (arctan(5/3)-arctan(3/2))
Using the formula of the tangent of the difference between two angles
we get
tan theta=(9/7-7/6)/(1+9/cancel(7)*cancel(7)/6)=((54-49)/42)/(1+3/2)=2/cancel5*cancel5/42=1/21
-> theta=arctan(1/21)
and
tan rho=(5/3-3/2)/(1+5/cancel3*cancel3/2)=((10-9)/6)/(1+5/2)=2/7*1/6=1/21
-> rho=arctan(1/21)
So
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