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y=tan^(-1)((acosx-bsinx)/(bcosx+asinx)),...

`y=tan^(-1)((acosx-bsinx)/(bcosx+asinx)), `where `-pi/2ltxltpi`and `a/btanx gt -1`.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`
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