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

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

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Statement 1: If agt0,bgt0, tan^(-1)(a/x)+tan^(-1)(b/x)=(pi)/2 . implies x=sqrt(ab) Statement 2: If m,n epsilonN,ngem, then "tan"^(-1)(m/n)+tan^(-1)(n-m)/(n+m)=(pi)/4 .

Prove that tan^(- 1)(1/3)+tan^(- 1)(1/7)+tan^(- 1)(1/13)+..........+tan^-1 (1/(n^2+n+1))+......oo =pi/4

Prove that: sum_(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2+n+2))

Prove that : sum_(m=1)^n\ \ \ tan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2+n+2))

The sides of a triangel are such that a/(1+m^2+n^2)=b/(m^2+n^2)=c/((1-m^2)(1+n^2)) , prove that A=2tan^-1 m/n, B=2tan^-1 (mn) and /_\ = (mnbc)/(m^2+n^2)

Prove that : tan^(-1) (e^(itheta)) = (n pi)/2 + pi/4 +i/2 ln" tan(pi/4 + theta /2) ,where n is an integer.

Prove that sum_(r=1)^(n) tan^(-1) ((2^(r -1))/(1 + 2^(2r -1))) = tan^(-1) (2^(n)) - (pi)/(4)

If a = x^(m + n) . Y^(l), b = x^(n + l). Y^(m) and c = x^(l + m) . Y^(n) , Prove that : a^(m-n) . b^(n - 1) . c^(l-m) = 1

If m tan(alpha-theta)/( cos^2 theta) = n (tan theta)/ (cos^2 (alpha - theta) the prove that 2 theta = alpha - [ tan^(-1) ((n-m)/(n+m)) tan alpha]

sum_(r=1)^nsin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1)))) is equal to (a) tan^(-1)(sqrt(n))-pi/4 (b) tan^(-1)(sqrt(n+1))-pi/4 (c) tan^(-1)(sqrt(n)) (d) tan^(-1)(sqrt(n)+1)

ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Simplify : tan ^(−1)(1/2)+tan ^(−1) (1/3).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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