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Let tan^(-1) y = tan^(-1) x + tan^(-1) (...

Let `tan^(-1) y = tan^(-1) x + tan^(-1) ((2x)/(1 -x^(2))), " where " |x| lt (1)/(sqrt3)`. Then a value of y is

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Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2)) , where |x|<1/(sqrt(3)) . Then a value of y is : (1) (3x-x^3)/(1-3x^2) (2) (3x+x^3)/(1-3x^2) (3) (3x-x^3)/(1+3x^2) (4) (3x+x^3)/(1+3x^2)

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ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. The value of cos^(-1)(-1)-sin^(-1)(1) is: a. pi b. pi/2 c. (3pi)/2 d. ...

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  2. The trigonometric equation sin^(-1) x = 2 sin^(-1) a has a solution fo...

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  3. If cos^(-1) x - cos^(-1).(y)/(2) = alpha, then 4x^(2) - 4xy cos alpha ...

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  4. If sin^(-1)(x/5)+cose c^(-1)(5/4)=pi/2 then a value of x is: (1) 1 (2...

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  5. The value of cot(cose c^(-1)5/3+tan^(-1)2/3) is: (1) 6/(17) (2) 3/...

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  6. If x, y, z are in A.P. and t a n^(-1)x ,""t a n^(-1)y"" and ""t a n^...

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  7. Let tan^(-1) y = tan^(-1) x + tan^(-1) ((2x)/(1 -x^(2))), " where " |x...

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  8. Prove that costan^(-1)sincot^(-1)x=sqrt((x^2+1)/(x^2+2))

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  9. If"sin"{cot^(-1)(x+1)}="cos"(tan^(-1)x), then find xdot

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  10. The value of the lim(n->oo)tan{sum(r=1)^ntan^(- 1)(1/(2r^2))} is equal...

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  11. Let (x, y) be such that sin^-1 (ax) + cos^-1 (bxy)=pi/2 If a=1 an...

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  12. Let (x , y) be such that sin^(-1)(a x)+cos^(-1)(y)+cos^(-1)(b x y)=pi/...

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  13. Let (x , y) be such that sin^(-1)(a x)+cos^(-1)(y)+cos^(-1)(b x y)=pi/...

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  14. about to only mathematics

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  15. The value of cot(sum(n=1)^23 cot^-1(1+sum(k=1)^n 2k)) is (a) 23/25 (b)...

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  16. (1/y^2 \ ((cos(tan^(-1) y) + y sin(tan^(-1) y))/(cot(sin^(-1) y) + tan...

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  17. lf cos x + cosy-cos z = 0 = sin x + sin y + sin z then cos((x-y)/2)=

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  18. If cos(pi/4-x)cos2x+sinxsin2xsecx=cos x sin 2x sec x+cos(pi/4+x)cos 2x...

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  19. If cot(sin^(-1)sqrt(1-x^2))=sin(tan^(-1)(xsqrt(6))),\ x!=0, then possi...

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  20. Let f:[0, 4pi]to[0, pi]" be difined by "f(x) = cos^(-1)(cos x). The nu...

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