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sec^2theta=(4x y)/((x+y)^2) is true if a...

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

A

` x + y ne 0`

B

`x =y , x ne 0, y ne 0`

C

x=y

D

`x ne 0, y ne 0`

Text Solution

Verified by Experts

The correct Answer is:
B
We know that , ` sec^(2) theta ge1 `
` (4xy)/((x+y)^(2)) ge 1 Rightarrow 4xy le (x+y)^(2)`
` Rightarrow (x-y)^(2) le 0`
`Rightarrow x -y=0`
` Rightarrow y =x and x ne 0, y ne 0`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-TRIGONOMETRIC FUNCTIONS -EXERCISE 2 (MISCELLANEOUS PROBLEMS)
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  4. If tantheta=(20)/(21) , show that (1-sintheta+costheta)/(1+sintheta...

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  5. For 0 le theta le pi/2 the maximum value of sin theta + cos theta i...

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  6. (cos 70^(@))/(sin 20^(@)) + (cos 59^(@))/(sin 31^(@) ) - 8 sin^(2) 30^...

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  7. If sin theta = 1/2 and theta is acute then (3 cos theta -4 cos^(3) ...

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  8. If 3 sin theta + 4 cos theta =5 , then value of sin theta is

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  9. If theta "is theta " and (cos^(2)theta)/(cot^(2) theta -cos^(2) theta)...

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  10. The value of (1+cos (pi/6))(1+cos(pi/3))(1+cos ((2pi)/3))(1+cos((7pi...

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  11. If cos 20^(@) - sin 20^(@) =p " then " cos 40^(@) is equal to

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  12. If Sn=cos^ntheta+sin^n tehta then find teh value of 3S4-2S6

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  13. If cos x + cos^(2) x =1 then the value of sin^(12) x + 3 sin^(10)...

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  14. If x sin^3theta+ycos^3theta=sinthetacostheta and xsintheta=ycostheta ...

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  15. If theta in the first quadrant and 5 tan theta =4 " then " ( 5 sin ...

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  16. If sinA+cosA=m and sin^3 A +cos^3 A = n then

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  17. If sintheta+cosectheta=2 then the value of sin^(10)theta+cosec^(10)the...

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

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  19. If sec theta + tan theta = k, cos theta equals to

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  20. ABC is a right angled isosceles triangle with /B=90^@ If D is a point ...

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