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The equation sec ^2 theta = ( 4xy )/...

The equation ` sec ^2 theta = ( 4xy )/( ( x+y)^2)` is possible for x,y, ` in R ` 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)
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  2. If sin^2theta=(x^2+y^2=1)/(2x) , then x must be -3 (b) -2 (c) 1 (d)...

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  3. The equation sec ^2 theta = ( 4xy )/( ( x+y)^2) is possible for x...

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  4. If sintheta1+sintheta2+sintheta3, then costheta1+costheta2+costheta3 i...

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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=1/5a n d0lt=theta<pi, then tantheta is -4/3 (b) ...

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  11. If pi,t h e nsqrt((1-cosalpha)/(1+cosalpha))+sqrt((1+cosalpha)/(1-cosa...

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  12. IF tan alpha = ( sin alpha - cos alpha )/( sin alpha + cos alpha)...

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  13. The least value of 2sin^2theta+3cos^2theta is 1 (b) 2 (c) 3 (d) ...

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  14. The greatest value of sin^4theta+cos^4thetai s 1/2 (b) 1 (c) 2 (d...

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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)+2sin^2theta is [3/4,1] (b)...

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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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