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If x be real show that costhetacannot be...

If x be real show that `costheta`cannot be equal to x+1/x.

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UNITED BOOK HOUSE-JODHPUR PARK BOYS'S SCHOOL-EXERCISE
  1. Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C....

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  2. Find the domain and range of the relation p defined by p={(a,b):b=|a...

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  3. If x be real show that costhetacannot be equal to x+1/x.

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  4. If costheta=tan^2((theta)/2)show that costheta=sqrt2-1

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  5. If tan15^@=x.then show that x^2+2sqrt3x-1=0

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  6. If omegabe an imaginaryb cube root of unity,then prove that,1/(1+2omeg...

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  7. Show that the middle term in the expansion of (x-1/x)^(2n)is (1.3.5.7....

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  8. Find the sum of all factors of the number 3645.

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  9. For any two positive numbers a and b,prove that AMgeGM

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  10. Find the vaue of 9^(1/3)9^(1/9)9^(1/27)...oo

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  11. Prove that the area of a triangle is invariant under the translation o...

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  12. If t1and t2 are the roots of the equation t^2+lambdat+1=0,where lambda...

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  13. Prove that Axx(BcupC)=(AxxB)cup(AxxC)

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  14. Find the distance from the eye at which a coin must be placed so as ju...

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  15. If cos(alpha+beta)=4/5.sin(alpha-beta)=5/13and alpha,betalie between 0...

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  16. Prove that cos((2pi)/7)+cos((4pi)/7)+cos((6pi)/7)=-1/2

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  17. Solve :6x^2-(5+3i)x+11i-3=0in the complex plane C.

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  18. Find the sum of first n terms of the series:1/(1+1^2+1^4)+2/(1+2^2+2^4...

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  19. Find n, if the ratio of the fifth term from beginning to the fifth ter...

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  20. Find the natural number a for which sum(k=1)^nf(a+k)=16(2^n-1)where th...

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