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If y = tan^(-1) ((a cos x - b sin x)/(b ...

If `y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)) " then " (dy)/(dx) =` ?

A

2

B

`-1`

C

`a/b`

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
`y=tan^(-1)""(a cosx-b sin x)/(b cos xx+a sin x)`
`=tan^(-1)""(((a)/(b)-tanx)/(a+a/btanx))`
`=tan^(-1)[tan{tan^(-1)((a)/(b))-x}]`
`impliesy=tan^(-1)""((a)/(b))-x`
`therefore (dy)/(dx)=0-1=-1`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 18-PAPER 2 (MATHEMATICS)
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  7. If A=[{:(6,8,5),(4,2,3),(9,7,1):}]then B =(A+A')/(2) is

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  8. If bar a,bar b and bar c are perpendicular ,bar c+bar a, bar b+bar c ...

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  9. The angle between the lines x^(2)+4xy+y^(2)=0 is

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  11. If in the figure shown A=1 and B=0, then oupput will be

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  12. If vec a , vec b ,a n d vec c be non-zero vectors such that no tow...

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  13. Area of the region bounded by the curve y={{:(x^(2)",",x lt0),(x",",...

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  14. The critical points of the function f(x)=2sin ^(2)((x)/(6))+sin((x)/...

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  15. int (2)^(3){x} dx is equal to (where {.} denotes, fractional part of ...

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  16. Let vecV=2hati+hatj-hatk and vecW=hati+3hatk. It vecU is a unit vector...

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  17. lim(x to oo) (1-(4)/(x-1))^(3x-1) is equal to

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  18. The middle point of chord x+3y=2 of the conic x^(2)+xy-y^(2)=1, is

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  19. If the sum of n terms of an A.P is 2n + 3n^2 , find the r^(th) term

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  20. Find the value of (320(32)^(1//6)(32)^(1//36)oodot

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