Inverse Trig Question (1 Viewer)

[echelon4]

show that tan^-1(4) - tan^-1(3/5) = 45degrees.

THanks in advanced

 

[Slidey]

Recognise that arctan(x) is actually an angle.

Now, take the tan of the LHS.

tan(arctan4-arctan3/5) requires use of the double angle formulae to expand:
[tan(arctan4)-tan(arctan3/5)]/[1+tan(arctan4).tan(arctan3/5)]
=(4-3/5)/(1+12/5)
=17/5/17/5
=1

But since we took the tan of the LHS, to get back to the original, we must take the inverse tan:
arctan(1)=pi/4=45 degrees

.'. arctan4 - arctan3/5 = 45 degrees

 

[echelon4]

ahhh, i c. THanks alot!!