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Prove the following: cos[tan^-1{sin(cot^...

Prove the following: `cos[tan^-1{sin(cot^-1x)}]=sqrt((1+x^2)/(2+x^2))`

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MODERN PUBLICATION-INVERSE-TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Let a and b be constants f(x) = a sin x + bx cos x + 2x^2 If f(3) = 15...

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  2. Number of solution of the equations: f(x-1) + f(x+1) = sin a, 0 < a , ...

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  3. If A={1,2,3}, B={1,3,5,7,9}, the ratio of number of one-one functions ...

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  4. The value of f(x) = x+2, then f(12)=K ,where K equals

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  5. If a , b are two natural numbers in AP such that a + b = 12 The ...

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  6. If a,b are positive number and product of ab= 2500.The minimum value o...

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  7. If f(x)^2 xx f((1-x)/(1+x)) = 64 x, x ne 0,1 then f(x) is equal to

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  8. If f(x)= 6x+9,then domain of f(x) is

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  9. A relation R on A={1,2,3} given by R={1,2), (1, 2), (3, 3)} is not sym...

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  10. Let ** be a binary operation on N given by a ** b= HCF (a, b), a, b, ...

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  11. Find the value of sin^(-1)(sin""(2pi)/(3))

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  12. Evaluate cot(tan^-1a +cot^-1a)

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  13. Show that the relation R defined by (a, b) R(c,d)implies a+d=b+c in...

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  14. Find fog if f(x) = |x| and g(x) = |5x-2|

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  15. Consider f : {1, 2, 3} rarr {a, b, c}, given by f (1) = a, f (2) = b ...

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  16. Let '*' be a binary operation on Q defined by a * b = (3ab)/5. Show th...

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  17. Prove that : tan^-1(1/2) + tan^-1(1/5) + tan^-1(1/8) = pi/4

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  18. find the value of x: 3 sin^-1(2x)/(1+x^2) - 4 cos^-1((1-x^2)/(1+x^2))...

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  19. Prove the following: cos[tan^-1{sin(cot^-1x)}]=sqrt((1+x^2)/(2+x^2))

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  20. Define a binary operation * on the set {0,1,2,3,4,5} as a*b = {:{(a+...

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