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The smallest positive integral value of ‘n’ such that `[(1+sin frac (pi)(8)+i cos frac (pi)(8))/(1+sin frac (pi)(8)-i cos frac (pi)(8))]^n` is purely imaginary is n =

A

2

B

6

C

4

D

3

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Prove that : 3 sin frac (pi)(6) sec frac (pi)(3)-4 sin frac (5pi)(6) cot frac(pi)(4)=1 .

Prove that sin frac (pi)(14) sin frac (3 pi)(14) sin frac (5pi)(14) sin frac (7pi)(14)=1/8 .

Prove that : (1+cos frac (pi)(8)) (1+cos frac (3pi)(8)) (1+cos frac (5pi)(8)) (1+cos frac (7pi)(8))=1/8 .

Prove that : sin^2 frac (pi)(8)+ sin^2 frac (3pi)(8)+ sin^2 frac (5pi)(8)+sin^2 frac (7pi)(8)=2 .

The value of : (1+cos frac (pi)(6)) (1+cos frac (pi)(3))(1+cos frac (2pi)(3)) (1+cos frac (7pi)(6)) is:

Prove that : sin frac (pi)(5) sin frac (2pi)(5) sin frac (3pi)(5) sin frac (4pi)(5) =5/16 .

Prove that : 16 cos frac (2pi)(15) cos frac (4pi)(15) cos frac (8pi)(15) cos frac (16pi)(15) =1.

Prove that: 2cos frac (pi)(13)cos frac (9pi)(13)+cos frac (3pi)(13)+cos frac (5pi)(13)=0

Prove that : sin^4 frac (pi)(8)+ sin^4 frac (3pi)(8)+sin^4 frac (5pi)(8)+sin^4 frac (7pi)(8)=3/2 .

Prove that : cos^2 frac (pi)(8)+ cos^2 frac (3 pi)(8)+ cos^2 frac (5 pi)(8) + cos^2 frac (7 pi)(8) =2 .

MODERN PUBLICATION-LINEAR INEQUATIONS-EXERCISE
  1. The complex number (1+2i)/(1-i) lies in:

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  2. If P is a point in the Argand diagram corresponding to the complex num...

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  3. The smallest positive integral value of ‘n’ such that [(1+sin frac (pi...

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  4. For (|x-1|)/(x+2) <1, x lies in the interval :

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  5. If a, b, c >0 and if abc=1, then the Value of a+b+c+ab+bc+ca lies in t...

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  6. Let z and w be two complex numbers such that |z|le1, |w|le1 and |z-iw|...

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  7. Find the range of f(x)=(x^2+34 x-71)/(x^2+2x-7)

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  8. If ax^2+bx+c=0 and 2x^2+3x+4=0 have a common root, where a, b, c in N ...

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  9. If (3+i)(z+bar z)-(2+i) (z- bar z)+14i=0, then z bar z =

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  10. 4+5((-1+i sqrt3)/2)^2008 +3((-1+i sqrt3)/2)^2009=

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  11. If the equation : (a +1) x^2 -(a+2)x+(a+3)=0 has roots equal in magni...

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  12. If alpha and beta are the roots of the quadratic equation x^2+4x+3=0,...

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  13. Which one of the following is one of the roots of the equation (b-c) x...

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  14. What is the value of x satisfying the equation : 16((a-x)/(a+x))^3= (a...

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  15. If alpha, beta are the roots of the equation : 2x^2-2(1+n^2)x+(1+n^2+n...

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  16. The roots of Ax^2 + Bx + C =0 are r and s. For the roots of x^2+ px + ...

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  17. What is the value of ((-1+i sqrt3)/2)^900+ ((-1-i sqrt3)/2)^301 ?

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  18. If 2^x+3^y =17 and 2^(x+2)-3^(y+1)=5, then what is the value of x ?

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  19. What is ((sqrt3+i))/((1+sqrt3 i)) equal to ?

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  20. If z1, z2, z3 are complex numbers such that |z1|= |z2|= |z3| =|1/z1+1/...

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