Find the value of
tan inverse { x + sqrt(1+x^2) }

tan-1x + 1+x2put x = tan θNow, tan-1tan θ + 1+tan2θ= tan-1tan θ + sec θ=tan-1sin θ + 1cos θ=tan-11 + cosπ/2-θsinπ/2-θ=tan-12 cos2π/4-θ/22 sinπ/4-θ/2 . cosπ/4-θ/2=tan-1cotπ/4-θ/2=tan-1tanπ/4+θ/2=π4+θ2=π4+tan-1x2

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