Can You Solve this Trig Inverse Equation with arctan and arctan?

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SUMMARY

The equation arctan(3x) + arctan(2x) = π/4 can be solved using the identity arctan[x] + arctan[y] = arctan[(x+y)/(1-xy)]. By applying this identity, the equation simplifies to 5x/(1-6x²) = 1. The solutions yield x = 1/6 and x = -1, with x = -1 being rejected due to the domain restrictions of the arctan function.

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Homework Statement


Solve arctan 3x + arctan 2x= pie/4?


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The Attempt at a Solution

 
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there is a trig identiy that helps.

arctan[x]+arctan[y] = arctan[(x+y)/(1-xy)]

then it is just the angle that has a tan of pi/4 (i am assuming radians), so 1

then solving 5x/(1-6x^2)=1 we get x= 1/6 and x=-1
reject the -1 as the domain of arctan does not include it if is re-inserted into the fuction.
 

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