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

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# Homework Help: An exponential problem and a trig problem

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