How to prove this trig equation

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The discussion revolves around proving the trigonometric identity cos(3x) = cos(x)(4cos²(x) - 3), which the user successfully accomplished. The second part of the question involves finding sin(π/10) and cos(π/10) without using a calculator, suggesting a connection to the first question. Participants indicate that the values can be derived from the earlier identity, hinting at a relationship between the angles. The user expresses confusion about how to relate the two questions effectively. The conversation emphasizes the importance of understanding trigonometric identities in solving related problems.
mohlam12
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hey
i have a problem with composed with two questions:
first i havr to prove that
cos(3x)=cos(x).(4cos^2(x) - 3)
okay, for this one, I was able to prove it; then the second question came, saying:
what is sin(pi/10) and cos(pi/10)
i don't know how to do that, but it should be related to the question before, how!? i don't know!
anyone with something to say ... ??
thanks
 
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From the information you have provided it seems like all you need to do is evaluate the sin and cos at \frac \pi {10}
 
but i can't use the calculator... because the second question doesn't say CALCULATE, in fact, it says NOTE from the previous question what sin and cos pi/10 is!
 
x = \frac \pi {10}
3x = \frac \pi {2} - 2x
 
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