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Question
Write the following function in the simplest form:
`tan^(-1) (sqrt((1 - cos x)/(1 + cos x)))`, 0 < x < π
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Solution
`tan^(-1) (sqrt((1 - cosx)/(1 + cosx)))`
= `tan^(-1) (sqrt((2sin^2 x/2)/(2cos^2 x/2)))`
= `tan^(-1) ((sin x/2)/(cos x/2)) `
= `tan^(-1) (tan x/2)`
= `x/2`
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