A Few Good Trig Identities

Geometry Level 2

11+sin2x+11+cos2x+12+tan2x+12+cot2x \dfrac { 1 }{ 1+\sin^{2} {x} } +\dfrac { 1 }{ 1+\cos^{2} {x} } +\dfrac { 1 }{ 2+\tan ^{2} {x} } +\dfrac { 1 }{ 2+\cot ^{ 2 }{ x } }

For all xx on the domain of the tanx\tan x and cotx,\cot x, what is the value of the expression above?

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