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If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, sho...

If `sin^(-1)x+sin^(-1)y+sin^(-1)z=pi`, show that `x^4+y^4+z^4+4x^2y^2z^2=2(x^2y^2+y^2z^2+z^2x^2)`

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ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that:tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=[pi/4m/n gt;-1(-3pi)/4m...

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  2. The sum of the infinte series sin^(-1)(1/sqrt(2))+sin^(-1)((sqrt(2)-1)...

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  3. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, show that x^4+y^4+z^4+4x^2y^2z^2=...

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  4. If alpha and beta are the roots of the equation x^2-4x + 1=0(alpha > ...

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  5. Solution set of inequality (cot^-1x)^2-5cot^-1x+6>0 is (A) (cot 3 ,...

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  6. Solve the following inequality: sin^(-1) x > cos^(-1) x

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  7. Solve the following system of inequations: 4(tan^(-1)x)^2-8tan^(-1)x+3...

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

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  9. Find all values of k for which there is a triangle whose angles have m...

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  10. Find the range of the function f(x)=(sin^(-1)x)^3+(cos^(-1)x)^3dot

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  11. Q.34 Q.34 Show that the roots r,s and t of the cubic Show that the roo...

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  12. The number of solutions of the equation |y|= cos x and y = cot^-1 (cot...

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  13. Solve for x : sin^(- 1)(sin((2x^2+4)/(1+x^2)))lt pi-3

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  14. Find the set of values of 'a' for which the equation 2cos^-1 x = a+a^2...

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  15. The value of cos^(-1)(-1)-sin^(-1)(1) is: a. pi b. pi/2 c. (3pi)/2 d. ...

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

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

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

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

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  20. 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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