Prove $\cos \frac{\pi}5-\cos \frac{2 \pi}5=\frac12$ but without finding $\cos \frac{ \pi}5$
How do we prove $\cos(\pi/5) - \cos(2\pi/5) = 0.5$ ?.
I couldn’t find any proof on the internet. I would appreciate an elementary proof , but any help would be appreciated!  Thank you. Why can't Inuzuka clan's dogs use human language? When did UX start being called UX? When did people start talking about User Experience as a role/domain similar to the way that it's used today?  The earliest reference I can find is the Norman, Miller, Henderson CHI 95 piece on Apple's set up (Donald Norman, Jim Miller, Austin Henderson: What You See, Some of What's in the Future, And How We Go About Doing It: HI at Apple Computer. Proceedings of CHI 1995, Denver, Colorado, USA)  Anything earlier?  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Limiting range of value types in C++ Suppose I have a LimitedValue class which holds a value, and is parameterized on int types 'min' and 'max'.  You'd use it as a container for holding values which can only be in a certain range.  You could use it such:  LimitedValue&lt; float, 0, 360 &gt; someAngle( 45.0 ); someTrigFunction( someAngle );   so that 'someTrigFunction' knows that it is guaranteed to be supplied a valid input (The constructor would throw an exception if the parameter is invalid).  Copy-construction and assignment are limited to exactly equal types, though.  I'd like to be able to do:  LimitedValue&lt; float, 0, 90 &gt; smallAngle( 45.0 ); LimitedValue&lt; float, 0, 360 &gt; anyAngle( smallAngle );   and have that operation checked at compile-time, so this next example gives an error:  LimitedValue&lt; float, -90, 0 &gt; negativeAngle( -45.0 ); LimitedValue&lt; float, 0, 360 &gt; postiveAngle( negativeAngle ); // ERROR!   Is this possible?  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