If $$\tan\theta =x $$ $$\theta=\frac{x}{tan(1)}$$ $$\theta=\frac{x}{\dfrac{\pi}4}$$ $$\pi\theta=4x$$ Is this valid?
I am learning inverse trigonometry but always my mind goes to these situations. So can somebody explain what limitations are there in inverse trigonometry functions?
Thanks!
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In the real numbers, the notation $a^{-1}$ means "multiplicative inverse" (i.e., "division".) In trigonometry, the notation $\tan^{-1}x$ doesn't not mean "multiplicative inverse." So the place where you try to divide both sides by $\tan$ doesn't work. Just as, in algebra, you computed inverse functions (using the notation $f^{-1}$), in trig, $\tan^{-1}$ is the inverse function, not the inverse of multiplication.
Your second step is completely wrong. You cant arrive from $\tan\theta =x$ to $\theta=\frac{x}{tan(1)}$. What you can get is If $\tan\theta =x$ then, $\theta=tan^{-1}(x)$