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The number of solutions of 2"cos"^(2)((x...

The number of solutions of `2"cos"^(2)((x)/(2))"sin"^(2) x =x^(2) + (1)/(x^(2)), 0 le x le (pi)/(2),` is

A

0

B

1

C

infinite

D

none of these

Text Solution

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Exercise
  1. If alpha is a root of 25"cos"^(2) theta+ 5"cos" theta-12 = 0, (pi)/(2)...

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  2. If "cos 3x + "sin" (2x - (7pi)/(6)) =-2, then x =

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  3. The number of solutions of 2"cos"^(2)((x)/(2))"sin"^(2) x =x^(2) + (1)...

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  4. If A and B are acute positive angles satisfying the equations 3 sin^(2...

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  5. The equation "sin" theta = x +(p)/(x) for real values of x is possible...

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  6. If sin A = sin B and cos A= cos B, then find the value of a in terms o...

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  7. Solve 5 cos 2 theta+2 "cos"^(2) theta/2 +1=0, -pi lt theta lt pi.

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  8. If (1+tantheta)(1+tanphi)=2, then theta + phi=

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  9. The general solution of "tan" 3x =1, is

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  10. If 1+sintheta+sin^2theta+sin^3theta+..to oo=4+2sqrt3 0<theta<pi, t...

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  11. If alpha a n d beta are the solutions of the equation at a ntheta+bs e...

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  12. Solve sinx+siny=sin(x+y)a n d|x|+|y|=1

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  13. The expression (1 + tan x + tan^2 x)(1-cot x + cot^2 x) has the positi...

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  14. If the the equation a sin x + cos 2x=2a-7 possesses a solution, then f...

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  15. The equation "sin"^(6) x + "cos"^(6) x = lambda, has a solution if

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  16. If y + "cos" theta = "sin" theta has a real solution, then

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  17. The solution set of the equation 4 sin theta. Cos theta-2 cos theta-2s...

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  18. The most general solution of tan theta =-1 and cos theta = 1/(sqrt(2))...

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  19. The complex numbers sin x +i cos 2x and cos x -i sin 2x are conjugate ...

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  20. The smallest positive root of the equation tanx-x=0 lies in (0,pi/2) ...

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