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Ifx+iy=3/(2+costheta+i sintheta)then sho...

If`x+iy=3/(2+costheta+i sintheta)`then show that `x^2 + y^2 = 4x - 3.`

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If x+iy=2/(3+costheta+isintheta) ,show that 2x^2+2y^2=3x-1

If x+iy=(3)/(2+cos theta + sin theta),"prove that" , x^(2)+y^(2)=4x-3.

If x+iy=(2)/(3+cos theta+isin theta),"show that" " " 2x^(2)+2y^(2)=3x-1.

(2+sqrt(3))costheta =1 - sintheta

Prove that if x=a(costheta+sin thetasin2theta) and y=a(sintheta+costhetasin2theta) ,then show that (x+y)^(2//3)+(x-y)^(2//3)=2a^(2//3)

If x=a(costheta+sinthetasin2theta)andy=a(sintheta+costhetasin2theta) , then show that (x+y)^((2)/(3))+(x-y)^((2)/(3))=2a^((2)/(3)) .

If P={theta:sintheta-costheta=sqrt2costheta} and Q={theta: sintheta+costheta=sqrt2 sintheta} , then show that P = Q.

If (3x-4y) prop sqrt(xy) then show that (x^2+y^2) prop xy .

If x costheta=y cos (theta+(2pi)/3)=z cos(theta+(4pi)/3) show that xy + yz+ zx = 0

IF 2 costheta=x+1/x then show that 2 cos3 theta=x^3+1/x^3

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 6-EXERCISE
  1. In any/\ABC, show that ‘c sin (A-B)/2=(a-b)cos(C/2)

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  2. Show that by mathematical induction, 3.5^(2n+1) + 2^(3n+1) is divisibl...

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  3. Ifx+iy=3/(2+costheta+i sintheta)then show that x^2 + y^2 = 4x - 3.

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  4. The sum of an infinite G.P series is 15 and the sum of the squares of ...

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  5. How many different arrangements be' possible in’EXAMINATION where two ...

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  6. A ray of light comming from (1, 2) to the x axis at A and reflecting w...

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  7. The co-ordinate of the two verties of a trainge are (15, 0) and (0 ,10...

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  8. Find the equation of the concentric- cricle of the circle x^2 + y^2 — ...

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  9. The distance between the point on x axis and (3, 2, —4) is m unit.Find...

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  10. Prove that,lim(nrarrprop)(1^3+2^3+3^3+....+n^3)/n^4=1/4

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  11. If y=(xsinx+cosx)/(xcosx-sinx),then show that dy/dx=x^2/(xcosx-sinx)^2

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  12. If n is a such real number that n>3 .then n^2>9 prove it by the method...

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  13. The mean and SD of 20 items were found to be 12.5 and 2.1 resp.After ...

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  14. Out of 15 articles in a box, three of. them are defective. If 5 articl...

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  15. In /\ABC,if (a^2+b^2)sin(A-B)=(a^2-b^2)sin (A+B),show that the triangl...

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  16. State the fundamental theorem of algebra Solve : ix^2 - x + 12i = 0

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  17. If S be the sum. P be the product,and R the sum of the reciprocals of ...

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  18. Exhibit graphically the solution region of the following system of 'in...

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  19. In quadrilateral PQRS, there are 3, 4, 5, 6 points are taken on PQ. QR...

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  20. If the extremitied of a focal chord of the parabola y^2=4axbe (at1^2,2...

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