Trigonometric Equation involving Tangent and Arctangent

Dear all,

For the following equation which I have to solve for , I am getting an expression that differs from the given answer and I do not understand why.

I have made two attempts, both posted below. Thank you very much for your help.

---

**Show: ** , where

---

__Solution 1: __

,

where I have used the facts that and took the arctangent of the original equation.

Re: Trigonometric Equation involving Tangent and Arctangent

Here's one way, though possibly not the best.

Also I think you meant for your fact.

But you may have forgot about

Re: Trigonometric Equation involving Tangent and Arctangent

Quote:

Originally Posted by

**scherz0** Dear all,

For the following equation which I have to solve for

, I am getting an expression that differs from the given answer and I do not understand why.

I have made two attempts, both posted below. Thank you very much for your help.

---

**Show: ** , where

---

__Solution 1: __ ,

where I have used the facts that

and took the arctangent of the original equation.

What they have done is recognised that , so must be in the second or fourth quadrants. Their solution only has the shift to the second quadrant (by subtracting from ).

Re: Trigonometric Equation involving Tangent and Arctangent