Inverse circular relations problems

Hey guys, my teacher gave me these two problems which have been keeping me up all night:

Prove:
[2tan^-1 (1/3) ]+ [tan^-1(1/7)] = pi/4

and

Find all values of θ:
Tan (π cot θ) = cot (π tan θ)

My classmates and I have been kinda stumped... Any help is much appreciated http://www.mymathforum.com/images/sm...on_biggrin.gif

Sincerely,
Carlos Jesena

Quote:

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Originally Posted by CarlosJesena

Hey guys, my teacher gave me these two problems which have been keeping me up all night:

[2tan^-1 (1/3) ]+ [tan^-1(1/7)] = pi/4

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Hint:

Spoiler:

Take the tangent of both sides and remember this

Quote:

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Find all values of θ:
Tan (π cot θ) = cot (π tan θ)

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Hint:

Spoiler:

and

Quote:

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Originally Posted by Drexel28

Hint:

Spoiler:

Take the tangent of both sides and remember this

Hint:

Spoiler:

and

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Thanks for the help! For this first problem, I turned it into 2A + B = pi/4 then that becomes tan (2A+B) = 1. Then I expanded the left side and got:

[tan(2A)+tan(B)] / [1-(tan(2A)tan(B))]

Am I on the right track? I was thinking of expanding the tan 2A's into double angle formula....

Quote:

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Originally Posted by CarlosJesena

Thanks for the help! For this first problem, I turned it into 2A + B = pi/4 then that becomes tan (2A+B) = 1. Then I expanded the left side and got:

[tan(2A)+tan(B)] / [1-(tan(2A)tan(B))]

Am I on the right track? I was thinking of expanding the tan 2A's into double angle formula....

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Yes, you're on the right track.

Quote:

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Originally Posted by Drexel28

Yes, you're on the right track.

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Thanks so much for the help! I get number one now. Just number two is still a mystery