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Prove that the identities, sin^-1 cos(s...

Prove that the identities, `sin^-1 cos(sin^-1x)+cos^-1 sin(cos^-1x)=pi/2`,`|x|<=1`

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ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Find the domain of definition the following function: f(x)=log(10)(1-l...

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  2. Simplify : tan ^(−1)(1/2)+tan ^(−1) (1/3).

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  3. Prove that the identities, sin^-1 cos(sin^-1x)+cos^-1 sin(cos^-1x)=pi...

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  4. Prove that:tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=pi/4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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