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Find the value of tan25°tan30°tan65°tan85°

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**atran****Member**- Registered: 2013-07-12
- Posts: 91

Start with, tan(x) = cot(90-x).

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Hmm......

I know but still tan30°tan85° remains.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**SteveB****Member**- Registered: 2013-03-07
- Posts: 577

tan(30) is 1/(square root of 3)

Not sure what is special about Tan(85). Looks like a rather horrible irrational number even when squared.

I do notice though that the other two multiply to leave 1.

(Tan(25) * Tan(65) = 1 I presume atran's trig. result proves it. Is this because 25+65 =90 ? and Tan(90-x) * Tan(x) = 1 etc.)

I notice that the gap between 85 and 90 is only 5. This is one sixth of the gap from 30 to zero.

I can tell from calculating the answer that it is not going to give us a whole number or the square root of a whole number.

Any idea what you are supposed to be trying to prove?

I have noticed that the angles 85 + 30 + 65 = 180

The three angles are interior angles of a triangle. I am not sure where this leads or whether it is relevant.

*Last edited by SteveB (2013-07-16 20:06:09)*

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