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If a gt b gt c gt0, then prove that cot^...

If `a gt b gt c gt0`, then prove that `cot^(-1) ((ab+1)/( a-b)) + cot^(-1) ((bc + 1)/( b-c)) + cot^(-1) ((ca + 1)/( c.-a)) = 0`

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Answer any three questions (e) If a gt b gt c gt0 , then prove that cot^(-1) ((ab+1)/( a-b)) + cot^(-1) ((bc + 1)/( b-c)) + cot^(-1) ((ca + 1)/( c'-a)) = pi

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Prove statement "tan"^(-1)((a-b)/(1+ab)) +"tan"^(-1)((b-c)/(1+bc)) ="tan"^(-1)a-"tan"^(-1) c .

Show that: tan^(-1)(a-b)/(1+ab)+tan^(-1)(b-c)/(1+bc)+tan^(-1)(c-a)/(1+ca)=0 .

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 10-SECTION B (60 MARKS)
  1. Answer any three questions (c) Show that f: [-1,1] to R, given by f(...

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  2. Show that the relation R in the set of real numbers, defined as R = {(...

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  3. If a gt b gt c gt0, then prove that cot^(-1) ((ab+1)/( a-b)) + cot^(-1...

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  4. A bag contains 6 black and 3 white balls. Another bag contains 5 black...

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  5. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  6. Answer any three questions (c) If [{:(2,-1),(1,0),(-3,4):}]A = [{:(-...

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  7. If A = [{:(2,5),(2,1):}] and B = [{:(4,-3),(2,5):}], verify that |AB| ...

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  8. The odds against A solving a certain problem are 4 to 3 and the odds i...

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  9. Find the equations of all the lines of slope 2 and that are tangent to...

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  10. Prove that the function f(x) = tan x -4x is strictly decreasing on (- ...

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  11. If y= cos^(-1) { 2x sqrt(1-x^(2) ) } , find (dy)/(dx).

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  12. If y = ( sin y )^(x), find (dy)/(dx).

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  13. Verify Rolle.s theorem for f(x) = (sin x)/( e^(x)) on 0 le x le pi.

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  14. Show that the function y=(A+Bx)e^(3x) is a solution of the equation (d...

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  15. Solve (x+1) (dy)/(dx) = 2xy.

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  16. Evaluate int e^(x) ((1- sin x)/( 1- cos x) ) dx

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  17. Find the area of the region bounded by the curve y=x^(3) and the lines...

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  18. Show that the points whose position vectors are 5hat(i) + 5 hat(k), 2 ...

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  19. Find the vector equation of the plane passing through the points 3 hat...

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  20. Prove that if a plane has the intercepts a, b, c and is at a distance ...

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