Question

solve the following :-
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Answer 1

Answer:

$\sqrt{ { \tan( \alpha ) }^{2} +{ \cot( \alpha ) }^{2} } = \sqrt{2}$

Step-by-step explanation:

$( \tan( \alpha ) + \cot( \alpha ) ) = 2 \\ \\ {( \tan( \alpha ) + \cot( \alpha ) )}^{2} = 4 \\ \\ { \tan( \alpha ) }^{2} + { \cot( \alpha ) }^{2} + 2 \tan( \alpha ) \cot( \alpha ) = 4 \\ \\ { \tan( \alpha ) }^{2} + \cot( \alpha ) + 2 = 4 \\ \\ \\ { \tan( \alpha ) }^{2} + { \cot( \alpha ) }^{2} = 4 - 2 \\ \\ { \tan( \alpha ) }^{2} + { \cot( \alpha ) }^{2} = 2 \\ \\ \\ \\ \sqrt{ { \tan( \alpha ) }^{2} +{ \cot( \alpha ) }^{2} } = \sqrt{2}$