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If y = {(1-tanx)/(1+tanx)}, show that (d...

If `y = {(1-tanx)/(1+tanx)}`, show that `(dy)/(dx) = (-2)/((1+sin2x))`.

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AI Generated Solution

To show that \(\frac{dy}{dx} = \frac{-2}{1 + \sin 2x}\) for the function \(y = \frac{1 - \tan x}{1 + \tan x}\), we will use the quotient rule for differentiation. ### Step-by-Step Solution: 1. **Identify the function**: \[ y = \frac{1 - \tan x}{1 + \tan x} \] ...
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Explore conceptually related problems

If y={(1-tan x)/(1+tan x)}, show that (dy)/(dx)=(-2)/(1+sin2x)

If y=(1-tanx)/(1+tanx) , prove that (dy)/(dx)=(-2)/(1+sin2x) .

Knowledge Check

  • If y=sqrt((1- tanx )/(1- tan x)) , then (dy)/(dx)=

    A
    `1/2 sqrt((1-tanx )/(1 + tan x)) sec^2 ((pi)/(4) +x)`
    B
    `sqrt((1- tan x)/( 1+ tan x )) sec^2 ((pi)/(4) +x)`
    C
    `1/2 sqrt((1- tan x)/(1+ tan x)) sec ""((pi)/(4) +x)`
    D
    None of these

  • int(1-tanx)/(1+tanx)dx=

    A
    `sec^(2)((pi)/(4)-x)+c`
    B
    `log(secx-sinx)+c`
    C
    `log(sinx+cosx)-k`
    D
    `log[sec((pi)/(4)-x)]+c`

  • If y=sqrt((1+tanx)/(1-tanx))," then: "(dy)/(dx)=

    A
    `(1)/(2)*sqrt((1-tanx)/(1+tanx))*sec^(2)((pi)/(4)+x)`
    B
    `sqrt((1-tanx)/(1+tanx))*sec^(2)((pi)/(4)+x)`
    C
    `(1)/(2)*sqrt((1-tanx)/(1+tanx))*sec((pi)/(4)+x)`
    D
    none of theses

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