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If tan^(-1)y=4tan^(-1)x(|x| < tan(pi/8))...

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

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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Solve for real values of x :((sin^(-1)x)^3+(cos^(-1)x)^3)/((tan^(-1)x+...

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  2. If x1, x2, x3,a n dx4 are the roots of the equations x^4-x^3sin2beta+...

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

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  4. Find the number of positive integral solution of the equation tan^(-1)...

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  5. Find the sum cos e c^(-1)sqrt(10)+cos e c^(-1)sqrt(50)+cos e c^(-1)sqr...

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  6. Find the domain for f(x)=sin^(-1)((1+x^2)/(2x))

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  7. If a,b,c be positive real numbers and the value of theta=tan^(- 1)sqrt...

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  8. If f(x)=sin^(-1)x then prove that lim(x-&gt;1/2)f(3x-4x^3)=pi-3lim(x-...

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  9. Solve sin^(-1)x-cos^(-1)x=sin^(-1)(3x-2)

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  10. Which of the following angles is greater? theta1=sin^(-1)(4/5)+sin^(-...

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  11. Find the value underset(n rarr oo)("lim") underset(k =2)overset(n)su...

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  12. If sin^(-1)((4x)/(x^2+4))+2tan^(-1)(-x/2) is independent of x , find t...

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  13. If cos^(-1)(6x)/(1+9x^2)=-pi/2+tan^(-1)3x , then find the value ofxdot

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  14. The greater of the two angles A=2tan^(-1)(2sqrt(2)-1) and B=3sin^(-1)(...

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  15. Find the range of f(X) =sin^(-1)x-cot^(-1)x+x^(2)+2x+6

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  16. Find the value of 2cos^(-1)3/(sqrt(13))+cot^(-1)(16)/(63)+1/2cos^(-1)7...

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  17. Prove that 2cos^(-1)x=sin^(-1)(2xsqrt(1-x^2))

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  18. Sove 2 cos^(-1) x = sin^(-1) (2 x sqrt(1 - x^(2)))

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  19. Find the domain for f(x)=sin^(-1)((1+x^2)/(2x))

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  20. Find the range of f(x)=cot^(-1)(2x-x^2)dot

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