Question

Tan a = root 2 -1. find the value of tan a - cot a?

Answer 1

Tan a =root2-1
Cot a=1/(root2-1)
Tan a - cot a
Root2-1 - 1/(root2-1)
(2-2root2+1-1)/root2-1
2 (1-root2)/root2-1
-2 (root2-1)/root2-1
-2
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Answer 2

$\tan( \alpha ) = \sqrt{2} - 1 \\ \tan( \alpha ) = \frac{1}{ \cot( \alpha ) } \\ \\\cot( \alpha ) = \sqrt{2} + 1 \\ \\ We've \: to \: find \: the \: value \: of \: , \\ \tan( \alpha ) - \cot( \alpha ) \\ \\ \tan( \alpha ) - \cot( \alpha ) = \sqrt{2} - 1 - \sqrt{2} - 1 \\ \\ \large \boxed{ \tan( \alpha ) - \cot( \alpha ) = - 2}$