Question

If tan x= √2-1 then proove that cot x =√2+1

Answer 1

Answer:

Step-by-step explanation:

tanX= √2-1

tanX = 1/cotX

tanX=1/√2-1

=1/√2-1 *√2+1/√2+1

tanX=1/√2+1

cotX=√2+1

Hence Proved

Answer 2

$\tan{x} = \sqrt{2} - 1 \\ \\ \Rightarrow \qquad \frac{1}{\tan{x}} = \frac{1}{\sqrt{2}-1} \\ \\ \Rightarrow \qquad \cot{x} = \frac{1}{\sqrt{2}-1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1} \qquad [\: \because \tan{\theta} = \frac{1}{\cot{\theta}} \:] \\ \\ \Rightarrow \qquad \cot{x} = \frac{\sqrt{2}+1}{(\sqrt{2}-1)(\sqrt{2}+1)} \\ \\ \Rightarrow \qquad \cot{x} = \frac{\sqrt{2}+1}{2-1} \qquad [\: \because (a+b)(a-b) = {a}^{2} - {b}^{2} \:] \\ \\ \Rightarrow \qquad \cot{x} = \sqrt{2} + 1 \\ \boxed{Hence, \; Proved}$