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Prove that 4sin27^@=sqrt(5+sqrt5)-sqrt(3...

Prove that `4sin27^@=sqrt(5+sqrt5)-sqrt(3-sqrt5)`

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UNITED BOOK HOUSE-MCQ-EXERCISE
  1. Prove that tan 20^@tan 40^@ tan 60^@ tan 80^@ = 3

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  2. If a sinalpha+bcosalpha=c and a cosecalpha+bsecalpha=c show thatsin2al...

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  3. Prove that 4sin27^@=sqrt(5+sqrt5)-sqrt(3-sqrt5)

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  4. Solve :tanx+tany=1,x+y=pi//4

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  5. If a^4+b^4+c^4+a^2b^2=2c^2(a^2+b^2),, then show thatangleC=60^@or120^@

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  6. Prove using principle of mathematical induction that sum of the cube t...

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  7. If x+iy=((a+ib)/(c+id))^(1//2),show that (x^2+y^2)=(a^2+b^2)/(c^2+d^2)

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  8. If one of the root of the equation px^2 + qx + r = 0 is the cube of th...

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  9. Solve graphically the following system of linear inequations - x - y l...

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  10. How many 4-digit numbers can be formed from the digits 1, 1, 2, 2, 3, ...

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  11. Prove that the middle term in the expansion of (1+x)^(2n)is(1.3.5........

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  12. If Sn be the sum of n consecutive terms of an A.P. show that S(n+4)-4S...

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  13. If n th term of a-series be (2.3^(n-1)+1),, find the sum of 1st r ter...

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  14. Show that the four straight lines xcosalpha+ysinalpha=P,xsinalpha-ycos...

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  15. Applying section formulae show that the points A(4. 7,-6), B (2, 5, -4...

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  16. Evaluate :lim(xrarry)(cos^2x-cos^2y)/(x^2-y^2)

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  17. Evaluate:lim(xrarr0)(sqrt(1+x^2)-sqrt(1+x))/(sqrt(1+x^3)-sqrt(1+x))

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  18. Evaluate: underset(x rarr 0)(lim)(e^(3x)-1)/(log(1+5x))

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  19. Evaluate :lim(xrarrpi//2)(xtanx-pi/2 secx)

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  20. Water is following into a right circular conical vassel. 45 cm deep an...

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