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If the roots of the quadratic equation `a(b-c)x^2+b(c-a)+c(a-b)=0`be equal then prove that a,b,c are in Harmonic progression .

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UNITED BOOK HOUSE-TIRTHAPATI INSTITUTION -EXERCISE
  1. If x costheta+ysintheta=xcosphi+ysinphithen show that y=x tan ((theta+...

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

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  3. Find the value of sin (221//2^@) with the help of the value of cos45^@

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  4. tan25^@=a prove that (tan155^@-tan115^@)/(1+tan155^@.tan115^@)=(1-a^2)...

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  5. Prove that,cos(pi/5)-cos((2pi)/5)=1/2

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  6. By the principle of mathematical induction prove that (5^(2n)-1)is alw...

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  7. IF x=a+bw+cw^2,y=a+bw^2+cwthen show that x^3+y^3=(2a-b-c)(2b-c-a)(2c-a...

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  8. If the roots of the quadratic equation a(b-c)x^2+b(c-a)+c(a-b)=0be eq...

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  9. Prove that (AcupB)^c=A^c capB^c[without venn-diagram]

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  10. If sinx-siny=a and cosx+cosy=b,prove that tan((x+y)/2)=+-sqrt((4-a^2-b...

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  11. Mathematically find the value of sin18^@

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  12. Show that cos(pi/11)cos((2pi)/11)cos((3pi)/11)cos((4pi)/11)cos((5pi)/1...

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  13. If cosx+cosy+cosz=0and sinx+siny+sinz=0then show that cos(x-y)+cos(y-z...

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  14. If z=x+iy and |2z-1| =|z-2|then prove that x^2+y^2=1

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  15. If the two roots of the quadratic equation ax^2+bx+c=0and alphaand bet...

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  16. For any three sets A,B,C prove by the formulae of set algebra that (Ac...

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  17. By the principle of mathematical induction prove that 1+2+3+4+…n=(n(n+...

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  18. Prove that tan1^@tan2^@tan3^@...tan88^@tan89^@=1

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  19. Show that tan50^@=tan40^@+2tan10^@

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  20. Show that sqrt3/(sin20^@)-1/(cos20^@)=4

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