Find the value of- tan -1cos x-sin x-cos x-sin x- for 0-x-

Tan^ 1 ( cos x sin x/cos x+sin x )=tan^ 1 ( cos x/cos x sin x/cos x/cos x/cos x+sin x/cos x ) (inside the bracket divide numerator and denominator by cosx) =tan ...

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Byju's Answer

Standard XII

Mathematics

Standard Formulae - 3

Find the valu...

Question

Find the value of,

$t a n^{- 1} (\frac{c o s x - s i n x}{c o s x + s i n x}$ ), for $0 < x < π$ .

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Solution

$t a n^{- 1} (\frac{c o s x - s i n x}{c o s x + s i n x}) = t a n^{- 1} (\frac{\frac{c o s x}{c o s x} - \frac{s i n x}{c o s x}}{\frac{c o s x}{c o s x} + \frac{s i n x}{c o s x}})$
(inside the bracket divide numerator and denominator by cosx)
$= t a n^{- 1} (\frac{1 - t a n x}{1 + t a n x}) = t a n^{- 1} [t a n (\frac{π}{4} - x)] [∵ t a n (\frac{π}{4} - x) = \frac{t a n \frac{π}{4} - t a n x}{1 + t a n \frac{π}{4} . t a n x} = \frac{1 - t a n x}{1 + t a n x}] = \frac{π}{4} - x$

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Similar questions

Q. Express

t a n^{- 1} (\frac{c o s x - s i n x}{c o s x + s i n x})

, for

0 < x < π

in the simplest form.

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{tan}^{- 1} \frac{cos x - sin x}{cos x + sin x}

w.r.t.

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Evaluate:

{tan}^{- 1} (\frac{cos x + sin x}{cos x - sin x})

Q. Solve

t a n^{- 1} {\frac{c o s x + s i n x}{c o s x - s i n x}}

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then find

\frac{d y}{d x}

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Find the value of, tan−1(cos x−sin xcos x+sin x), for 0<x<π.

tan−1(cos x−sin xcos x+sin x)=tan−1(cos xcos x−sin xcos xcos xcos x+sin xcos x) (inside the bracket divide numerator and denominator by cosx) =tan−1(1−tan x1+tan x)=tan−1[tan(π4−x)][∵tan(π4−x)=tanπ4−tan x1+tanπ4.tan x=1−tan x1+tan x]=π4−x

Find the value of,

$t a n^{- 1} (\frac{c o s x - s i n x}{c o s x + s i n x}$ ), for $0 < x < π$ .