Home
Class 12
MATHS
If x=secvarphi-tanvarphi and dy=cosecvar...

If `x=secvarphi-tanvarphi and dy=cosecvarphi+cotvarphi,` then (a)`x=(y+1)/(y-1)` (b) `x=(y-1)/(y+1)` (c)`y=(1+x)/(1-x)` (d) `x y+x-y+1=0`

A

`x=(y+1)/(y-1)`

B

`x=(y-1)/(y+1)`

C

`y=(1+x)/(1-x)`

D

`xy+x-y+1=0`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
We have `x=(1-sinphi)/(cosphi),y=(1+cosphi)/sinphi`
Multiplying, we get
`xy=((1-sinphi)(1+cosphi))/(cosphisinphi)`
`rArr xy+1=(1sinphicosphi=sinphicosphi)/(cosphisinphi)`
`=(1-sinphi+cosphi)/(cosphisinphi)`
`andx-y=((1-sinphi)sinphi-cosphi(1+cosphi))/(cosphisinphi)`
`=(sinphi-sin^2phi-cosphi-cos^2phi)/(cosphisinphi)`
`=(sinphi-cosphi-1)/(cosphisinphi)=-(xy+1)`
Thus, `xy+x-y+1=0, x=(1+x)/(1-x)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Matrix)|3 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise (Single)|57 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

If y = tan^(-1) ((1+ x)/(1-x)). find y' .

If y=tan^(-1)((1+x)/(1-x)) find y'.

(1 + e^(x/y)) dx + e^(x)/(y)(1 - (x)/(y)) dy = 0

(dy)/(dx) = y tan x, y = 1 when x = 0

If y = (sin^(-1) x)/(sqrt(1-x^2)) show that (1-x^2) y_2 - 3xy_1 - y =0

If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s (a) x/(2y-1) (b) x/(2y+1) (c) 1/(x(2y-1)) (d) 1/(x(1-2y))

If sinx+cosx=sqrt(y+1/y) for x in [0,pi] , then (a) x=pi/4 (b) y=0 (c) y=1 (d) x=(3pi)/4

(dy)/(dx)+(3y)/(x)=(1)/(x^(2)) , given that y = 2 when x = 1.