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Prove that : tan^-1((cosx)/(1+sinx)) = p...

Prove that : `tan^-1((cosx)/(1+sinx)) = pi/4 - x/2, x in (-pi/2,pi/2)`

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MODERN PUBLICATION-INVERSE-TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. show that tan^-1(1/2) + tan^-1(1/5) + tan^-1(1/8) = pi/4

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  2. If tan^-1((x-2)/(x-4)) + tan^-1((x+2)/(x+4)) = pi/4 find the value of ...

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  3. Prove that : tan^-1((cosx)/(1+sinx)) = pi/4 - x/2, x in (-pi/2,pi/2)

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  4. Show that 2sin^-1(3/5)-tan^-1(17/31) = pi/4

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  5. Prove that : tan^-1 x +tan^-1 2x/(1-x^2) = tan^-1 ((3x-x^3)/(1-3x^2)),...

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  6. If tan^-1 x + tan^-1y - tan^-1z = 0, then prove that x + y + xyz = z.

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  7. Let f(x) = sin (pi/6 sin (pi/2 sinx)) for all x inR and g(x) = pi/2 si...

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  8. If alpha = 3 sin^(-1) (6/11) " and "beta = 3 cos^(-1) (4/9) , where ...

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  9. Let f:(-1,1)vecR be such that f(cos4theta)=2/(2-sec^2theta) for theta ...

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  10. Let f(-pi/2,pi/2) rarr R be given by (log(sec x + tan x))^3. Then

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  11. A function f: Z rarrrZ is defined as below f(x) = {:{(x+3, if x is od...

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  12. The number of linear functions satisfying f(x+f(x))=x+f(x),forall x ...

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  13. If cot^-1 7 + cot^-1 8 + cot^-1 18 = cot^-1 k, then k is

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  14. If f: R rarrR satisfying:f(x-f(y)) = f(f(y) +f(x)-1, for all x, y in R...

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  15. Let a and b be constants f(x) = a sin x + bx cos x + 2x^2 If f(3) = 15...

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

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

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

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

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

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