Proving Trig Equations:

Question

jadedry · Answer

Can you tell I'm having a lot of trouble with this section? Question coming in a sec!

jadedry · Answer

$$2 \arctan \frac{ 1 }{ 2 } = arcos \frac{ 3 }{ 5 }$$

jadedry · Answer

*Prove the above!

So far I tried: $$2 \tan x = \cos y $$

So: $$1 = 3/5 ?$$

Obviously I'm not going about this the right why, but I'm kind of at a loss here.

jadedry · Answer

Alternatively I tried:

$$2 \arctan 1/2 - \arccos 3/5 = 0  = 2x-y = 0 = \cos (2x-y) = \pi/2$$

jadedry · Answer

$$= \cos 2x \cos y + \sin 2x \sin y = \pi/2$$

jadedry · Answer

If tan x = 1/2 and cos y = 3/5

sin x = 1/5 , cos x = 2/5

sin y = 4/5 , tan y = 4/3

etc etc, until I could replace all the values in the above equations with the relevant trig values. But I came up with 1/5 , which seems...unrelated to pi/2

jadedry · Answer

Help would be greatly appreciated, I'm really battling with this. ;n;