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Write the Function in the Simplest Form: Tan^(-1) ((Cos X - Sin X)/(Cos X + Sin X)) 0 < X < Pi - Mathematics

Sum

Write the function in the simplest form:  `tan^(-1)  ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`

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Solution

`tan^(-1)  (cos x - sin x)/(cos x + sin x)`

Dividing cos x inside

`= tan^(-1) [((cos x- sin x)/cos x)/((cos x + sinx)/cosx)]`

`= tan^(-1) [(cos x/cos x - sin x/cos x)/(cos x/cos x + sin x/cosx)]`

`= tan^(-1)  (1 - tan x)/(1 + tan x)`

`= tan^(-1)  [(1 - tan x)/(1+1. tan x)]`

`= tan^(-1) [(tan pi/4 - tan x)/(1 + tan pi/4 . tan x)]`     (As  tan `pi/4` = 1)

`= tan^(-1) tan (pi/4 - x)`

`= pi/4 - x`

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APPEARS IN

NCERT Class 12 Maths
Chapter 2 Inverse Trigonometric Functions
Q 8 | Page 47
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