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Geometry Level 4

$\large{\frac{\tan3x-\tan2x}{1+\tan3x \tan2x}=1}$

The set of values of $x$ for which they satisfy the equation is? In the options stated $n\in \mathbb Z$

n\pi +\frac{\pi}{4}

The empty set:

\phi

2n\pi+\frac{\pi}{4}

\frac{\pi}{4}

2 solutions

Tanishq Varshney
Apr 16, 2015

using $\tan(A-B)=\frac{\tan A-\tan B}{1+\tan A \tan B}$

we get $\tan(3x-2x)=1$

$\tan x=1$

$x=n\pi+\frac{\pi}{4}$

but

$\tan2x$ is not defined at $x=n\pi+\frac{\pi}{4},~n\in \mathbb Z$

For example if $x=\frac{\pi}{4}$ then $\tan(2x)=\tan(\frac{\pi}{2})$

Hence $\tan2x$ is not defined so no solution exist

Nicely done. A common mistake students made is they fail to check back whether their solution actually works.

Lmao this problem destroyed my rating.

Kunal Verma - 6 years, 1 month ago

Now i did explain it

Tanishq Varshney - 6 years, 1 month ago

I don't understand. Why tan2x influences to the answer. I still think that x=n.pi+pi/4.

Hafizh Ahsan Permana - 6 years, 1 month ago

U will surely agree to that the solution of any equation we find must satisfy that equation.

since $\tan(\frac{\pi}{2})=\infty$

If we put $x=\frac{\pi}{4}$

then the expression reduces to $\frac{-\infty}{\infty}$ which is an indeterminant form

Tanishq Varshney - 6 years, 1 month ago

@Tanishq Varshney – Got it. Thanks.. I was trapped hhe.

Hafizh Ahsan Permana - 6 years, 1 month ago

Nice question. Got tricked though...

neelesh vij - 5 years, 5 months ago

Ahmed Moh AbuBakr
Apr 18, 2015

that mean x=45 so tan(2x=90)=1/0 so it can't be done

This solution has been marked wrong. How did you reach the conclusion that that "x=45" and "it can't be done"?

Let me clear it." X=45" means X=pi/4 and "it can't be done" means that the condition is undetermined. It is just language problem Challenge Master.

Hafizh Ahsan Permana - 6 years, 1 month ago

thanks >> i am not very good at explaining :)

Ahmed Moh AbuBakr - 6 years, 1 month ago

that i get it from the tan rule

Ahmed Moh AbuBakr - 6 years, 1 month ago

challenge master so troll

Rutwik Dhongde - 6 years, 1 month ago