Question

value of cot 405....
plz anwer fast​

Answer 1

Answer:

$\cot \left(405^{\circ \:}\right)=1$

Step-by-step explanation:

$\cot \left(405^{\circ \:}\right)$

$\gray{\mathrm{Rewrite\:the\:angles\:for}\:\cot \left(405^{\circ \:}\right):}$

$\gray{\cot \left(405^{\circ \:}\right)=\cot \left(\frac{8+1}{4}180^{\circ \:}\right)=\cot \left(\left(\frac{8}{4}+\frac{1}{4}\right)180^{\circ \:}\right)=\cot \left(180^{\circ \:}\cdot \:2+\frac{1}{4}180^{\circ \:}\right)}$

$=\cot \left(180^{\circ \:}2+\frac{1}{4}180^{\circ \:}\right)$

$\gray{\mathrm{Use\:the\:periodiciity\:of\:}\cot :\quad \cot \left(x+180^{\circ \:}\cdot \:k\right)=\cot \left(x\right)}$

$\gray{\cot \left(180^{\circ \:}\cdot \:2+\frac{1}{4}180^{\circ \:}\right)=\cot \left(\frac{1}{4}180^{\circ \:}\right)}$

$=\cot \left(\frac{1}{4}180^{\circ \:}\right)$

$\gray{\mathrm{Simplify}}$

$=\cot \left(45^{\circ \:}\right)$

$\gray{\mathrm{Use\:the\:following\:trivial\:identity}:\quad \cot \left(45^{\circ \:}\right)=1}$

$=1$