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Prove that cot^(-1)(13)+cos^(-1)(21)+cot...

Prove that `cot^(-1)(13)+cos^(-1)(21)+cot^(-1)(-8)=pi`.

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ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. If tan^(- 1)((2x)/(x^2-1))+cos^(- 1){(x^2-1)/(x^2+1)}=(2pi)/3 then ...

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  2. Find the sum of the series :tan^- 1(1/3)+tan^- 1(2/9)+....+tan^- 1((2^...

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  3. Prove that cot^(-1)(13)+cos^(-1)(21)+cot^(-1)(-8)=pi.

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  4. Find the sum of each of the following series :(i) tan^-1(1/(x^2+x+1))+...

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  5. Find the domain of definition the following function: f(x)=log(10)(1-l...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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