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If tan^(-1)y=4tan^(-1)x, (|x| lt tan(pi...

If `tan^(-1)y=4tan^(-1)x, (|x| lt tan(pi) /8)` , find `y` as an algebraic function of `x` , and , hence, prove that `tan(pi/8)` is a root of the equation `x^4-6x^2+1=0`

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ALLEN -INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. The complete solution set of the inequality [cot^(-1)x]^2-6[cot^(-1)x]...

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  2. If cot^(-1)(n/pi)>pi/6,n in N , then the maximum value of n is 6 (b) ...

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  3. If tan^(-1)y=4tan^(-1)x, (|x| lt tan(pi) /8) , find y as an algebraic...

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  4. If A=2tan^(-1)(2sqrt(2)-1) and B=3sin^(-1)(1/3)+sin^(-1)(3/5), then wh...

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  5. If [sin^-1 (cos^-1(sin^-1 (tan^-1 x)))]=1, where [*] denotes the gre...

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  6. Transform sin^(-1)x in other inverse trigonometric function.

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  7. The value of sin^(-1)(-sqrt(3)/2)\ is: (A) (-pi)/3 (B) (-2pi)/3 (...

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  8. cos(2 tan^(-1)(1/7))equals: a."sin"(4cot^(-1)3) b. "sin"(3cot^(-1)4)...

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  9. The value of sec(sin^-1sin((-50pi)/9)+cos^-1cos((31pi)/9))

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  10. cos (cos^-1 cos((8pi)/7) +tan^-1 tan((8pi)/7)) has the value equal to ...

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  11. (sin^(-1) x)^2 + (sin^(-1) y)^2 + 2(sin^(-1) x)(sin^(-1) y) = pi^2 , t...

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  12. If cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x , then sinx is ...

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  13. "tan"(cos^(-1)x) is equal to a.x/(1+x^2) b. (sqrt(1+x^2))/x c.(sqrt(...

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  14. If x=2cos^(-1)(1/2)+sin^(-1)(1/(sqrt(2)))+tan^(-1)(sqrt(3))\ a n d\ y=...

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  15. If x=tan^(- 1)(1)+cos^(- 1)(-1/2)+sin^(- 1)(-1/2) and y=cos[1/2cos...

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  16. tan^(-1)2+tan^(-1)3=cos e c^(-1)x ,then x is equal to a.-(19)/(40) b...

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  17. If sin^(-1)x+cot^(-1)(1/2)=pi/2,\ t h e n\ x is a. 0 b. 1/(sqrt(5)) c....

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  18. If tan(cos^(-1)x)="sin"(cot^(-1)(1/2)) then x is equal to- a.1/sqrt(5)...

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  19. sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x is true if x in a. [0,\ 1]\ b. [...

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  20. Domain of the explicit from of the function y represented implicity by...

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