The reason the latter can be denoted $\tan^2 x$ is because functions form an associative algebra under composition, for which composition is like a multiplication of functions And if you multiply the tangent function by itself, you're squaring it. If $\theta$ is exactly $90^\circ$, then $\tan \theta$ is undefined because of division by zero. If $\theta$ tends to $90^\circ$, namely $\theta -90^\circ$ is (non-zero) infinitesimal, then $\tan\theta=\infty$. You said: as $\frac {1} {0}$ could be both positive and negative infinity This is correct only when you clearly understand its meaning. $\frac {1} {0}$ is not valid as an arithmetic. How do i find the solutions to the equation $$\\tan x= x$$ upto any number of decimals Of course, there is the graphical method but it just helps in finding the approximate value. However, you can only take a couple derivatives of tan (x) before it becomes unbearable to calculate
Is there a relatively easy way to find the maclaurin polynomial of tan (x)? An easy, mostly graphical proof The reason you get a division by zero in the argument of arctan is that $\displaystyle\lim_ {\varphi\to\frac\pi2}\tan\varphi=\pm\infty\approx\tfrac10$ 1 use tan (a+b) formula and remember tan (ix) = i tanhx use that in your formula and then simplify as you would normal complex numbers if you need a detailed answer let me know cheers Recall that cosine is an even and sine an odd function It follows from the basic properties of real numbers that the quotients $\sin x / \cos x$ and $\cos x / \sin x$ are odd.
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