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If ci >0 for i=1,2,....., n prove that ...

If `c_i >0` for `i=1,2,....., n ` prove that `tan^(-1)((c_1x-y)/(c_1y+x))+tan^(-1)((c_2-c_1)/(1+c_2c_1))+tan^(-1)((c_3-c_2)/(1+c_3c_2))+.........+``tan^(-1)(1/(c_n))=tan^(-1)(x/y)`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. If a , b , c >0 and s=(a+b+c)/2, prove that tan^(-1)sqrt((2a s)/(b c...

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  2. If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+...

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  3. If ci >0 for i=1,2,....., n prove that tan^(-1)((c1x-y)/(c1y+x))+tan^...

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  4. Evaluate: tan^(-1)(1)+tan^(-1)(0),

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

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  6. Sum the following series to infinity: tan^(-1)1/(1+1+1^2)+tan^(-1)1/(1...

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  7. Solve the equation: tan^-1(2x)+tan^-1 {(3x)} =pi/4

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  8. If a1,a2,a3, an are in arithmetic progression with common difference d...

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  9. Prove that: tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x...

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  10. If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)...

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  11. Find the maximum and minimum values of (sin^(-1)x)^3+(cos^(-1)x)^3, wh...

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  12. the greatest and least values of (sin^(-1) x)^2+(cos^(-1)x)^2

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  13. Solve : 4sin^(-1)x=pi-cos^(-1)x

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  14. If (sin^(-1)x)^2+(cos^(-1)x)^2=(17pi^2)/(36) , find xdot

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  15. Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4

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  16. Prove that : tan^(-1)(2/11)+tan^(-1)(7/24)=tan^(-1)(1/2)

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  17. Prove that: sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi

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  18. Prove that: tan^(-1)1+tan^(-1)2+tan^(-1)3=pi

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  19. Prove that: tan^(-1)(1/7)+tan^(-1)(1/(13))=tan^(-1)(2/9) tan^(-1)(1...

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  20. If tan^(-1)2+tan^(-1)3+theta=pi, find the value of thetadot

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