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Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1...

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
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  2. If cos^(- 1)x-cos^(- 1)(y/2)=alpha then 4x^2-4xycosalpha+y^2=

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

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

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

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  6. Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2)) , where |x|<1/(sqrt(3))...

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

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  8. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

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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 (ax) + cos^-1 (bxy)=pi/2 If a=1 an...

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

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  14. If 0 < x <1, then sqrt(1+x^2)[{xcos(cot^-1x)+sin(cot^-1 x)}^2-1]^(1/2)...

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  15. The value of cot(sum(n=1)^2 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]->[0,pi] be defined by f(x)=cos^-1(cos x). The number ...

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