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If x is not an integral multiple of 2 pi...

If x is not an integral multiple of `2 pi`, use Mathematical Induction to prove that : `cos x+cos 2x+.............+cos nx= cos frac (n+1)(2) x sin frac (nx)(2) cosec frac (x)(2)`.

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MODERN PUBLICATION-LINEAR INEQUATIONS-EXERCISE
  1. Let z=x+iy be a complex number, where x and y are integers and i=sqrt(...

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  2. If |z-4/z|=2 then the greatest value of |z| is:

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  3. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, t...

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  4. The number of complex numbersd z, such that abs(z-1)=abs(z+1)=abs(z-i)...

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  5. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+tz(2...

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  6. Let alpha and beta be real and z be a complex number. If z^(2)+az+beta...

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  7. If omega( ne 1) is a cube root of unity and (1+omega)^(7)=A+bomega, th...

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  8. By Mathematical Induction, prove that : n! <((n+1)/2)^n , n>1.

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  9. By Mathematical Induction, prove that : (1+1/n)^n len for all nge3.

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  10. By Mathematical Induction, prove the following : (4^n+ 15n -1) is di...

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  11. Given n^4 <10^n for a fixed integer nge 2. Prove that (n+1)^4 <10^(n+1...

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  12. When P is natural number , then P^(n+1)+(P+1)^(2n-1) is divisible by

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  13. Using Mathematical Induction, prove that : "^mC0 ^nCk+ ^mC1 ^nC(k-1)+....

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  14. If x is not an integral multiple of 2 pi, use Mathematical Induction t...

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  15. Find theta such that (3+2i sin theta)/(1-2i sin theta) is purely real.

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  16. Find all circles which are orthogonal to |z|=1and|z-1|=4.

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  17. If the complex variables z1,z2 and origin form an equilateral triangle...

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  18. Let the complex numbers z1,z2,z3 be the vertices of an equilateral tri...

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  19. Let A and B be two complex numbers such that A/B+B/A=1. Prove that the...

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  20. Let A, B, C, D and E be points on the complex plane, which respectivel...

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