# Trigonometry problem

#1
Hi, I would really appreciate your help with this problem :

arctan x + arccos x = pi/4

Thank you
0
7 years ago
#2
(Original post by Melanie Leconte)
Hi, I would really appreciate your help with this problem :

arctan x + arccos x = pi/4

Thank you
What have you tried?
0
7 years ago
#3
You can use compound angle formulae; for instance try taking the tangent of both sides of the equation.
0
#4
Thank you. I have tried using some of the trigonometric identities including the sum & difference formulas for sin, cos and tan.
0
7 years ago
#5
(Original post by Melanie Leconte)
Hi, I would really appreciate your help with this problem :

arctan x + arccos x = pi/4

Thank you
Assuming that you want to solve for , then this question would be easier if it were all in terms of, say, arctan. So suppose that and try to find an expression that introduces somehow. (Hint: draw an appropriate right angled triangle).
0
#6
(Original post by Mr M)
What have you tried?

Thank you. I have tried using some of the trigonometric identities including the sum & difference formulas for sin, cos and tan.
0
7 years ago
#7
(Original post by Melanie Leconte)
Thank you. I have tried using some of the trigonometric identities including the sum & difference formulas for sin, cos and tan.
The easiest way is to tan both sides and use the expansion of tan (A+B).

http://en.wikipedia.org/wiki/Inverse...tric_functions
0
7 years ago
#8
(Original post by Melanie Leconte)
Hi, I would really appreciate your help with this problem :

arctan x + arccos x = pi/4

Thank you
Did you manage to solve this? I get the only solution to be but that's by way of a messy quartic, one of whose roots I had to find via Wolfram alpha, and which can be ruled out by a non-trivial argument about the behaviour of over (or which in fact I did by checking its graph)

This seems far too tricky for A level - is it a STEP question?
0
#9
(Original post by atsruser)
Did you manage to solve this? I get the only solution to be but that's by way of a messy quartic, one of whose roots I had to find via Wolfram alpha, and which can be ruled out by a non-trivial argument about the behaviour of over (or which in fact I did by checking its graph)

This seems far too tricky for A level - is it a STEP question?

I don't know if it is from step paper. I was set it as a brain teaser for year 11.
I have managed to solve it and I can see what you mean about the quartic
0
7 years ago
#10
(Original post by Melanie Leconte)
I don't know if it is from step paper. I was set it as a brain teaser for year 11.
I have managed to solve it and I can see what you mean about the quartic
Where do you study that you do this in year 11? Hogwarts?
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