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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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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.

'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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**SteveB****Member**- Registered: 2013-03-07
- Posts: 576

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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