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Question
Write the following function in the simplest form:
`tan^(-1) (sqrt((1-cos x)/(1 + cos x))), x < pi`
Solution
`tan^(-1) (sqrt((1-cos x)/(1+ cos x))), x < pi`
`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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