If $$cot2$$⁡$$x=$$$$cot$$⁡(x$$−$$y)$$cot$$⁡(x$$−$$z) ,then $$cot2x$$ is equal to (where$$ x≠±π$$/4)

Question

If $$cot2$$⁡$$x=$$$$cot$$⁡(x$$−$$y)$$cot$$⁡(x$$−$$z) ,then $$cot2x$$ is equal to (where$$ x≠±π$$/4)

Infinity Learn · Accepted Answer

$$cot2$$⁡$$x=$$$$cot$$⁡(x$$−$$y)$$cot$$⁡(x$$−$$z)or$$ $$cot2$$⁡$$x=$$$$cot$$⁡xcot⁡$$y+1cot$$⁡y−$$cot$$⁡xcot⁡xcot⁡$$z+1cot$$⁡z−$$cot$$⁡xor  $$cot2$$⁡xcot⁡ycot⁡z−$$cot3$$⁡xcot⁡y−$$cot3$$⁡xcot⁡$$z+cot4$$⁡x $$=cot2$$⁡xcot⁡ycot⁡$$z+$$$$cot$$⁡xcot⁡$$y+$$$$cot$$⁡xcot⁡$$z+1or$$  $$cot3$$⁡$$x($$$$cot$$⁡$$y+$$$$cot$$⁡$$z)+$$$$cot$$⁡$$x($$$$cot$$⁡$$y+$$$$cot$$⁡$$z)+1$$−$$cot4$$⁡$$x=0or$$  $$cot$$⁡$$x($$$$cot$$⁡$$y+$$$$cot$$⁡$$z)1+cot2$$⁡$$x+1$$−$$cot2$$⁡$$x1+cot2$$⁡$$x=0or$$  $$cot$$⁡$$x($$$$cot$$⁡$$y+$$$$cot$$⁡$$z)+1$$−$$cot2$$⁡$$x=0or$$  $$cot2$$⁡x−$$12cot$$⁡$$x=12($$$$cot$$⁡$$y+$$$$cot$$⁡$$z)

If $\cot^{2} x = \cot (x - y) \cot (x - z)$ ,then cot2x is equal to (where $x \neq \pm π / 4$ )

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If cot2⁡x=cot⁡(x−y)cot⁡(x−z) ,then cot2x is equal to (where x≠±π/4)

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If $\cot^{2} x = \cot (x - y) \cot (x - z)$ ,then cot2x is equal to (where $x \neq \pm π / 4$ )