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sec^2 x=(4xy)/(x+y)^2 is true if and onl...

`sec^2 x=(4xy)/(x+y)^2` is true if and only if

A

`x+yne0`

B

`x=y,xne0`

C

`x=y`

D

`xne0,yne0`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `sec^2theta=(4xy)/((x+y)^2ge1`
Now `sec^2thetage1rArr(4xy)/((x+y)^2ge1`
`or (x+y)^2le4xy`
`or (x+y)^2-4xyle0`
`or (x-y)^2le0`
But for real values of x and y,
`(x-y)^2ge0or(x-y)^2=0`
`:. x=y`
Also `x+yne0rArrxne0.yne0`
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CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
  1. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

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  2. if sin^2theta=(x^2+y^2+1)/(2x) then x must be

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  3. sec^2 x=(4xy)/(x+y)^2 is true if and only if

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  4. If sintheta1+sintheta2+sintheta3=3," then "costheta1+costheta2+costhet...

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  5. If sinx+siny+sinz+sinw=-4" then the value of "sin^400x+sin^300y+sin^20...

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  6. The minimum value of the expression sin alpha + sin beta+ sin gamma, ...

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  7. If 1+sinx+sin^2x+sin^3x+oo is equal to 4+2sqrt(3),0<x<pi, then x is eq...

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  8. The value of expression (2sin^2 91^0-1)(2sin^2 92^0-1)(2sin^2 180^0-1)...

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  9. If sinA=sin^2B and 2cos^2A=3cos^2B then the triangle ABC is

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  10. If sintheta+costheta=1/5and 0lethetaltpi" then "tantheta is

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  11. If piltalphalt(3pi)/2lt" then "sqrt((1-cosalpha)/(1+cosalpha))+sqrt((1...

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  12. If 0 < alpha < pi/ 6 then alpha(cosec alpha) is

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  13. The least value of 2sin^2theta+3cos^2theta is

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  14. The greatest value of sin^4theta+cos^4theta is

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  15. If f(x)=sin^6x+cos^6x , then range of f(x) is [1/4,1] (b) [1/4,3/4] ...

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  16. The minimum value of atan^2x+bcot^2x equals the maximum value of asin^...

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  17. Range of f(theta)=cos^2theta(cos^2theta+1)+2 sin^2theta is

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  18. If 0<theta<pi, then minimum value of 3sintheta+cos e c^3theta is 4 (b)...

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  19. If thetaigt0" for "1lethetalenandtheta1+theta2+theta3+...+thetan=pithe...

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  20. The set of values of lambda in R such that sin^2theta+costheta=lambda...

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