Question and Answers Forum

All Questions      Topic List

UNKNOWN Questions

Previous in All Question      Next in All Question      

Previous in UNKNOWN      Next in UNKNOWN      

Question Number 79437 by Vishal Sharma last updated on 25/Jan/20

The value of tan 1° tan 2° tan 3°...tan 89°  is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\:\mathrm{1}°\:\mathrm{tan}\:\mathrm{2}°\:\mathrm{tan}\:\mathrm{3}°...\mathrm{tan}\:\mathrm{89}° \\ $$$$\mathrm{is} \\ $$

Commented by mr W last updated on 25/Jan/20

=1  since tan (x)×tan (90−x)=1

$$=\mathrm{1} \\ $$$${since}\:\mathrm{tan}\:\left({x}\right)×\mathrm{tan}\:\left(\mathrm{90}−{x}\right)=\mathrm{1} \\ $$

Commented by mathmax by abdo last updated on 25/Jan/20

A =tan((π/(180))).tan(((2π)/(180))).....tan(((89π)/(180)))  we have tan(((89π)/(180)))=tan((π/2)−(π/(180)))=(1/(tan((π/(180)))))  tan(((88π)/(180)))=tan((π/2)−((2π)/(180)))=(1/(tan(((2π)/(180))))) ....⇒A =1

$${A}\:={tan}\left(\frac{\pi}{\mathrm{180}}\right).{tan}\left(\frac{\mathrm{2}\pi}{\mathrm{180}}\right).....{tan}\left(\frac{\mathrm{89}\pi}{\mathrm{180}}\right) \\ $$$${we}\:{have}\:{tan}\left(\frac{\mathrm{89}\pi}{\mathrm{180}}\right)={tan}\left(\frac{\pi}{\mathrm{2}}−\frac{\pi}{\mathrm{180}}\right)=\frac{\mathrm{1}}{{tan}\left(\frac{\pi}{\mathrm{180}}\right)} \\ $$$${tan}\left(\frac{\mathrm{88}\pi}{\mathrm{180}}\right)={tan}\left(\frac{\pi}{\mathrm{2}}−\frac{\mathrm{2}\pi}{\mathrm{180}}\right)=\frac{\mathrm{1}}{{tan}\left(\frac{\mathrm{2}\pi}{\mathrm{180}}\right)}\:....\Rightarrow{A}\:=\mathrm{1} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com