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If omegabe an imaginaryb cube root of un...

If `omega`be an imaginaryb cube root of unity,then prove that,`1/(1+2omega)+1/(2+omega)-1/(1+omega)=0`

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UNITED BOOK HOUSE-JODHPUR PARK BOYS'S SCHOOL-EXERCISE
  1. If costheta=tan^2((theta)/2)show that costheta=sqrt2-1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. The line joing two points A(2,0)and B(3,1)I rotated about A in anti cl...

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  19. In what direction should a line be drawn through the pont (1,2) so tha...

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  20. If (alpha^2,alpha)lies inside the triangle bounded by the lines x-5y+6...

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