Home
Class 12
MATHS
"If "y=tan^(-1)((a cos x- b sin x)/(b co...

`"If "y=tan^(-1)((a cos x- b sin x)/(b cos x + a sin x)), "where "-(pi)/(2)ltxlt(pi)/(2)" and "(a)/(b) tan x gt-1, " then find "(dy)/(dx).`

Text Solution

Verified by Experts

`"Let "y=tan^(-1)((a cos x- b sin x)/(b cos x + a sin x)),`
`=tan^(-1)(((a)/(b)-tan x)/(1+(a)/(b) tan x))`
`=tan^(-1)((a)/(b))-tan^(-1)(tan x)`
`=tan^(-1)((a)/(b))-x" "[because-(pi)/(2)ltxlt(pi)/(2)`
`therefore" "(dy)/(dx)=0-1=-1`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Solved Examples|28 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.1|1 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • DOT PRODUCT

    CENGAGE ENGLISH|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If y = sqrt((cos x - sin x)(sec 2x + 1)(cos x + sin x)) , Then (dy)/(dx) at x = (5 pi)/(6) is :

If y = sqrt((cos x - sin x)(sec 2x + 1)(cos x + sin x)) , Then (dy)/(dx) at x = (5 pi)/(6) is :

If 2y=(cot^(-1)((sqrt3 cos x + sin x)/(cos x - sqrt3 sin x)))^(2) , x in (0, pi/2) " then " (dy)/(dx) is equal to

x=a cos t, y=b sin t find dy/dx

Show that '(1-cos 2x + sin x)/(sin 2x + cos x) = tan x'

If y=sin^(-1)x+cos^(-1)x ,\ find (dy)/(dx) .

If y = tan ^(-1) (sec x + tan x) , " find " (d^(2) y)/( dx^(2)) at x = (pi)/(4)

If y=sin^(-1)(sin x), then dy/dx at x =pi/2 is

Solve cos^(-1) (cos x) gt sin^(-1) (sin x), x in [0, 2pi]

If 0 lt x lt pi and cos x + sin x = 1/2 , then tan x is