Prove without using a calculater that

 

cos36 -cos72 =1/2

The most sentient thing i can say atm is that 72 is an angle twice as big as 36

Are you familiar with any trig identities?

Also, are you familiar with the word please?

Prove without using a calculater that

 

cos36 -cos72 =1/2

Well, because it is?

 

Going from the fact that 36 is one-half of 72, I would assume that cos25 - cos50 is also 1/2?

Well, because it is?

 

Going from the fact that 36 is one-half of 72, I would assume that cos25 - cos50 is also 1/2?

 

I agree with your very valid point "because it is", but unfortunately cos25 - cos50 isn't equal to 1/2, it's closer to 0.2635

Trig functions are not linear.

 

The easiest way to do this is to memorize all of the values of cosine for the various fractional values of pi. Otherwise I assume it's fair game that you know that pi/6 gives 1/2, and use the angle addition and subtraction formulae.

How many fractional values would that be? A couple of dozen?

 

Maybe I should study maths. It sounds easy enough, except my brain doesn't have enough RAM to handle numbers over single digits...

cos(36) - cos(72) = 0.40347889260888592

cos(36) - cos(72) = 0.40347889260888592

 

No, it's 0.5

 

36 and 72 degrees. I don't get your answer even in radians, so I don't know where you made your mistake.

How many fractional values would that be? A couple of dozen?

 

Maybe I should study maths. It sounds easy enough, except my brain doesn't have enough RAM to handle numbers over single digits...

 

Every 15 degrees has a "special" representation

 

[math]\sin(\frac{\pi}{12} = 15\deg) = \frac{\sqrt{2}}{4} (\sqrt{3}-1) = \frac{\sqrt{6}-\sqrt{2}}{4}[/math]

 

[math]\sin(\frac{\pi}{6} = 30\deg) = \frac{{1}}{2}[/math]

 

[math]\sin(\frac{\pi}{4} = 45\deg) = \frac{\sqrt{2}}{2}[/math]

 

[math]\sin(\frac{\pi}{3} = 60\deg) = \frac{\sqrt{3}}{2}[/math]

 

[math]\sin(\frac{5\pi}{12} = 75\deg) = \frac{\sqrt{2}}{4} (\sqrt{3}+1) = \frac{\sqrt{6}+\sqrt{2}}{4}[/math]

 

[math]\sin(\frac{\pi}{2} = 90\deg) = 1[/math]

Prove without using a calculater that

 

cos36 -cos72 =1/2

 

maybe you can prove this by using logorythm tables but those are extinct i say go with what eveyone says cos72=cos2(36) but without a calculators is very much impossible for most since we have no values to work with and no idea what cos36 is.