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

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

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  2. Find the sum of infinite series s = sin^(-1) ( 1/sqrt2) + sin ^(-1) ...

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

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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. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

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  12. Thee value of cos ^(−1 )x+cos ^(−1)( x/2​ + root(3-x^2)/2−x2 ​ ), wh...

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

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  14. Solve sin^(-1)[((2x^2+4)/(1+x^2))]<pi-3

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

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

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

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

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

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