3
votes
3answers
161 views

Validity of a trigonometric proof that $2 = 0$.

I can't find where this proof goes wrong. We know $$\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A\cdot\tan B}$$ so $$\begin{align} \tan(90^\circ-45^\circ) &= \frac{\tan 90^\circ -\tan ...
0
votes
1answer
49 views

Where exactly is the following process incorrect to yield an impossible answer

I was playing with my calculator and found some strange phenomena. $\cos(\tan(\tan(\tan(\pi/4)))) = 0.75686700166$ Verify here Now when we apply some inverses, then $\tan(\tan(\tan(\pi/4))) = ...
7
votes
1answer
94 views

Prove $\frac {1}{\cos 0^\circ \cdot \cos 1^\circ} + \ldots +\frac {1}{\cos 88^\circ \cdot \cos 89^\circ}= \frac{\cos 1^\circ}{\sin 1^\circ}$

Prove the following identity: $$\frac {1}{\cos 0^{\circ} \cdot \cos 1^{\circ}} + \ldots +\frac {1}{\cos 88^{\circ} \cdot \cos 89^{\circ}} = \frac{\cos 1^{\circ}}{\sin 1^{\circ}}$$ After hours of ...
4
votes
2answers
219 views

$x \sin x=2$ why is my proof that there no solutions wrong?

$\frac 12 x \sin x=1$ . Let's look at a right triangle with base $x$ and altitude $\sin x$ . Then our equation is for the area of this triangle. Let the sides of the triangle be $a=x$ , $b=\sqrt ...
13
votes
12answers
3k views

Funny thing. Multiplying both the sides by 0?

Alright this maybe really funny but I want to know why is this wrong. We often come across identities which we prove by multiplying both the sides of the identity by a certain entity but why don't we ...
1
vote
2answers
279 views

Vector Identity and the Scalar Product

Ok, I have a question that probably has a very simple answer but for some reason I can't see it. Let $a$ and $r$ be two vectors of nonzero length with a common origin and let $\theta$ be the nonzero ...
4
votes
1answer
506 views

What's wrong with this proof that $e^{i\theta} = e^{-i\theta}$?

I recently learned that $\cos{\theta} = \frac{e^{i\theta} + e^{-i\theta}}{2}$ and $\sin{\theta} = \frac{e^{i\theta} - e^{-i\theta}}{2}$ Based on this, I managed to "prove" that: $$e^{i\theta} = ...