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If f(x) =(1-x^2)/(1+x^2), prove that f ...

If `f(x) =(1-x^2)/(1+x^2)`, prove that `f (tan theta)= cos 2 theta`.

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MODERN PUBLICATION-RELATIONS AND FUNCTIONS -EXERCISE
  1. If f(x) =(1-x^2)/(1+x^2), prove that f (tan theta)= cos 2 theta.

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  2. If A = { a, b,c}, B = {p,q}, find BxxA .

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  3. Let A = {1, 2, 3, 4,5,6} and B = {2,4,6, 8}. Find A xx B .

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  4. Find x and y if : (x+1,y -2) = (3,1)

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  5. Find x and y if : (x+ 2,4) = (5, 2x+ y)

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  6. If (x/3+1, y-2/3)=(5/3, 1/3), find the values of x and y.

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  7. Let A= {1, 2, 3,4} and S = {(a, b) : a in A, b in A, a divides b}. Wri...

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  8. Let A = {1, 2} and B = {3, 4}. Write A xx B. How many subsets will A x...

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  9. Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y...

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  10. If the set A has 3 elements and the set B = {3, 4, 5}, then find the n...

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  11. The Cartesian product A xx A has 9 elements among which are found (-1,...

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  12. If A= {-1, 1}, find A xx A xx A.

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  13. If R is the set of all real numbers. what do the cartesian products R ...

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  14. If A xx B = {(a, x).(a , y). (b, x), (b, y)}. Find A and B.

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  15. If A = { 1, 2}, B = {3, 4}, C = {4, 5}, find A xx (B uu C).

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  16. If A={a, b,c}, B= {c, d} and C= {d, e, f}, find : (A nn B)xxC.

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  17. If A={a, b,c}, B= {c, d} and C= {d, e, f}, find : (A xx B) nn (BxxC).

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  18. Let A = {1, 2, 4}, B= {3, 5, 7} and C = {5, 7, 9}, find A xx (B nn C).

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  19. Let A= {1, 2, 3}, B= {3, 4} and C = {4, 5, 6}. Find : (A xx B) nn (Ax...

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  20. Let A= {1, 2, 3}, B= {3, 4} and C = {4, 5, 6}. Find : (A xx B) nn (Ax...

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  21. Let A= {1, 2, 3}, B= {3, 4} and C = {4, 5, 6}. Find : Axx (B uu C).

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