Solve Arctan 2Arctan(1/3) + Arctan(1/7) = π/4: What's Wrong?

[Alexx1]

2Arctan(1/3) + arctan(1/7) = π/4

I try to solve it like this:

= sin(2arctan(1/3)) + sin(arctan(1/7) = sin(π/4)

But this isn't correct

What have I done wrong?

 

[rock.freak667]

2Arctan(1/3) + arctan(1/7) = π/4

I try to solve it like this:

= sin(2arctan(1/3)) + sin(arctan(1/7) = sin(π/4)

But this isn't correct

What have I done wrong?

If we let A=Arctan(1/3) and B= arctan(1/7), then tanA=1/3 and tanB=1/7 right?

So now you have 2A+B=π/4, what happens if you take the tan of both sides?

 

[Mentallic]

2Arctan(1/3) + arctan(1/7) = π/4

I try to solve it like this:

= sin(2arctan(1/3)) + sin(arctan(1/7) = sin(π/4)

But this isn't correct

What have I done wrong?

The problem is that $$sin(A+B)\neq sinA+sinB$$ for all A and B, which is what you've done on the left side of the equation.
Since you took the sine of both sides, it should be $$sin\left(2arctan(1/3)+arctan(1/7)\right)=sin(\pi/4)$$
and from the mistake above that I showed you, you can't separate each part in the sine to make two sine functions as you've done.

Try follow on and see where rockfreak is leading you. You need to know how to expand tan double angles and sums.

 

[Alexx1]

The problem is that $$sin(A+B)\neq sinA+sinB$$ for all A and B, which is what you've done on the left side of the equation.
Since you took the sine of both sides, it should be $$sin\left(2arctan(1/3)+arctan(1/7)\right)=sin(\pi/4)$$
and from the mistake above that I showed you, you can't separate each part in the sine to make two sine functions as you've done.

Try follow on and see where rockfreak is leading you. You need to know how to expand tan double angles and sums.

Thanks! Now I found it