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**nurshodiq****Member**- Registered: 2009-03-29
- Posts: 12

1. find value of

2. find value of

3. if , prove

4. if , prove

*Last edited by nurshodiq (2009-06-04 13:20:41)*

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**baskar****Member**- Registered: 2009-06-07
- Posts: 3

answer for (1) find the value of cos^2 (18) + cos^2 (54):

cos^2 (18) = [10+2 sqrt(5)]/16 = 0.9045085

we know cos3x = 4cos^3 (x) - 3cos(x)

=> cos(54) = 4 cos^3 (18) - 3cos(18) = 4 (0.74001063) - 3 (0.9045085)

=> cos(54) = 2.96004252 - 2.71352550 = 0.24651702

=> cos^2 (54) = (0.24651702)^2 = 0.06077

=> cos^2 (18) + cos^2 (54) = 0.9045085 + 0.0607700 = 0.9652785

cheers, baskar

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**nurshodiq****Member**- Registered: 2009-03-29
- Posts: 12

thanks baskar, i had answer for #1. but different with yours,

*Last edited by nurshodiq (2009-06-09 17:44:24)*

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**Kurre****Member**- Registered: 2006-07-18
- Posts: 280

*Last edited by Kurre (2009-06-10 04:01:21)*

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**Kurre****Member**- Registered: 2006-07-18
- Posts: 280

I wanted to find a solution that uses the result from problem 3, which took a while and is probably not the easiest one, but here it is anyway:

*Last edited by Kurre (2009-06-10 04:19:38)*

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**nurshodiq****Member**- Registered: 2009-03-29
- Posts: 12

i have a way to answer #4,

if

and

, so we have

multiple both sides by 4 we have

thanks

*Last edited by nurshodiq (2009-06-11 01:25:02)*

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