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Prove that 1+cotthetalt=cottheta/2for0<t...

Prove that `1+cotthetalt=cottheta/2for0

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We have
`1+cot theta-cot""(theta)/(2)=1+(cot^(2)""(theta)/(2)-1)/(2 cot"" (theta)/(2))-cot""(theta)/(2)`
`=(2 cot ""(theta)/(2)+cot^(2)""(theta)/(2)-1-2cot^(2)""(theta)/(2))/(2 cot ""(theta)/(2))`
`=(-(cot"" (theta)/(2)-1)^(2))/(2 cot"" (theta)/(2))le 0` for `0lt thetaltpi`.
or `1+cot thetale cot ""(theta)/(2)`
Equaility holds when `cot"" (theta)/(2)-1=0` or `theta=(pi)/(2)`.
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