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The equation sin^2theta=(x^2+y^2)/(2x y)...

The equation `sin^2theta=(x^2+y^2)/(2x y),x , y!=0` is possible if

A

x = y

B

x = - y

C

2x = y

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Now, `sin^2theta=(x^2+y^2)/(2xy)`
`:. ` x,y have same sign
Now `(x^2+y^2)/(2xy)=1/2[(sqrt(x/y)-sqrt(y/x))^2+2]ge1`
But `sinthetale1," Therefore", (x^2+y^2)/(2xy)=1`
`rArrx=y`.
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CENGAGE-TRIGONOMETRIC FUNCTIONS -Exercise (Single)
  1. Given that the side length of a rhombus is the geometric mean of the ...

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  2. Which of the following is correct?

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  3. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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