Yesterday in a math competition, I came across two problems that I couldn't (and still can't) figure out how to solve under the competion conditions (in under three minutes, without using a calculator).(adsbygoogle = window.adsbygoogle || []).push({});

The first one involved expential functions. When I try to do it I just get a huge mess of exponents and logs that takes me forever to simplify. It is as follows:

9^x + 9^-x = 34, evaluate 3^x+3^-x

The second problem involved trig functions:

Find the exact value of cot 15 + cot 75

Are there sum and difference formulas for cot? I tried turning the cot into cos/sin and then adding the fractions. That left me with

[tex] \frac{\sin(15)\cos(75)+\cos(15)\sin(75)}{\sin(75)\sin(15)} [/tex]

Using the sum formula this would become

[tex]\frac{\sin 90}{\sin(75)\sin(15)} = \frac{1}{\sin(75)\sin(15)} [/tex]

Can I do anything with this?

Thanks for your help!

Tom

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# An exponential problem and a trig problem

**Physics Forums | Science Articles, Homework Help, Discussion**