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Question
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
Solution
Let y = `tan^-1sqrt((1 - cos x)/(1 + cos x)`
[1 – cos 2θ = 2 sin2θ and 1 + cos 2θ = 2 sin2 θ]
y = `tan^-1 sqrt((2 sin^2 x/2)/(2 cos^2 x/2))`
y = `tan^-1 sqrt(tan^2 x/2)`
y = `tan^-1(tan x/2)`
y = `x/2`
`("d"y)/("d"x) = 1/2 xx 1 = 1/2`
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