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प्रश्न
Express `tan^-1 ((cos x - sin x)/(cos x + sin x))`, 0 < x < π in the simplest form.
उत्तर
Consider `((cos x - sin x)/(cos x + sin x))`
Dividing the numerator and denominator by cos x.
we get `(((cosx)/(cosx) - (sin x)/(cosx))/((cos x)/(cos x) + (sin x)/(cosx)))`
`= (1 - tan x)/(1 + tan x)`
`= (tan pi/4 - tan x)/(1 + tan pi/4 tan x)`
`[because tan pi/4 = 1]`
`= tan (pi/4 - x) [because tan ("A - B") = (tan "A" - tan "B")/(1 + tan "A" tan "B")]`
`therefore tan^-1 [tan (pi/4 - x)]`
`= pi/4 - x`
which is the simplest form.
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