Question

solve the trigonometric equation. tan (pi/2-x) + tan (-x)= 0

Answer 1

is \[\tan (\frac{ \pi }{ 2}-x)+\tan(x) or \tan(\frac{ \pi }{ 2-x })+\tan(x)?\]?

Answer 2

if is the firts, the answer is X=pi/4 but if is the second the answer is a little complicated.

Answer 3

it is the first and I know the answer but i want to know how to do it

Answer 4

well first apply tan^-1(argument) or arctan that is the reverse of tangent, then \[\tan^-1(\tan(\frac{ \pi }{ 2 }-x))=\tan^-1(\tan(x))\]
\[\frac{ \pi }{ 2 }-x=x \] so u can clear the x\[\frac{ \pi }{ 2 }=2x \]
then x=pi/4