Finding tan(5) in terms of p when p=tan(10)

[MathsHelpPlz]

Tan(10)=p find the value of tan(5) in terms of p.

I know the addition formula tan(A+B)=(tan(A)+tan(B))/(1-tan(A)tan(B)) but I don't know how to apply it to this situation.

Thanks for your time.

EDIT: I know how to use the double angle formula for this situation but I can't figure out how to use the addition formula.

 

[pka]

Tan(10)=p find the value of tan(5) in terms of p.

Let $\displaystyle q=\tan(5^o)$ then $\displaystyle p=\dfrac{2q}{1-q^2}$.

Solve for $\displaystyle q$.

 

[MathsHelpPlz]

Let $\displaystyle q=\tan(5^o)$ then $\displaystyle p=\dfrac{2q}{1-q^2}$.

Solve for $\displaystyle q$.

Hi, thanks for the reply. I know how to do it that way, but I am unsure how to do it other ways such as using expansions of tan(60-55) or tan(15-10).

 

[Deleted member 4993]

Tan(10)=p find the value of tan(5) in terms of p.

I know the addition formula tan(A+B)=(tan(A)+tan(B))/(1-tan(A)tan(B)) but I don't know how to apply it to this situation.

Thanks for your time.

EDIT: I know how to use the double angle formula for this situation but I can't figure out how to use the addition formula.

I am not sure - why you are stuck!!

You know:

tan(A+B)=(tan(A)+tan(B))/(1-tan(A)tan(B))

set A = B = 5°

then

tan(5+5)=(tan(5)+tan(5))/(1-tan(5)tan(5))

tan(10) = 2*tan(5)/(1-tan²(5))

assume

tan(10) = p and tan(5) = q, then

p = 2*q/(1-q²)

This is a quadratic equation in q, solve for q.

 

[Deleted member 4993]

Hi, thanks for the reply. I know how to do it that way, but I am unsure how to do it other ways such as using expansions of tan(60-55) or tan(15-10).

But you were to use only one information → tan(10) = p

Is there more to the problem statement than you have posted?

 

[MathsHelpPlz]

But you were to use only one information → tan(10) = p

Is there more to the problem statement than you have posted?

That's all there is to the question, it's just that the mark scheme posted several ways of doing the question, the other ways I don't understand

It's question 9 on http://www.ocr.org.uk/images/57765-question-paper-unit-4723-01-core-mathematics-3.pdf
and the mark scheme is on page 12 of the document (page 15 according to Adobe PDF Reader) on http://www.ocr.org.uk/images/57748-mark-scheme-january.pdf But I guess if I can do the question it doesn't really matter