# Thread: Write trig expression as an algebraic expression containing u and v

1. ## Write trig expression as an algebraic expression containing u and v

I'm stuck on this one:
Cos(tan^-1u+tan^-1v)
I know you can use cos(a+b)=cosacosb-sinasinb but not sure what to do after.

2. ## Re: Write trig expression as an algebraic expression containing u and v

Hey av66.

I think you may want to draw two triangles with angles u and v in them and use the same ideas that you use to solve something like cos(tan^(-1)[u]) or sin(tan^(-1)[u]).

3. ## Re: Write trig expression as an algebraic expression containing u and v

Thanks! I think I got it now. Is the answer?:
(1-uv)/(√1+u^2√1+v^2)

4. ## Re: Write trig expression as an algebraic expression containing u and v

I haven't done the working out but if you want to get the opinions of other readers (including myself) then show us the working out so we can follow and evaluate it.

5. ## Re: Write trig expression as an algebraic expression containing u and v

I understand, here's a picture of my work. If you could please check the next question also.

6. ## Re: Write trig expression as an algebraic expression containing u and v

Hello, av66!

Is the answer? .$\displaystyle \frac{1-uv}{\sqrt{1+u^2}\sqrt{1+v^2}}$
Yes . . . Good work!