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

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))+\ dot+tan^(-1)(1/(c_n))=tan^(-1)(x/y)`

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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
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  15. Solve for x :tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x ,x >0

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  17. Solve for x : tan^(-1)(x+2)+tan^(-1)(x-2)=tan^(-1)(8/(79)) , x >0

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  18. Solve for x : tan^(-1)(x/2)+tan^(-1)(x/3)=pi/4 , 0

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  19. Solve for x : tan^(-1)((x-2)/(x-1))+tan^(-1)((x+2)/(x+1))=pi/4

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  20. Solve for x : tan^(-1)(2+x)+tan^(-1)(2-x)=tan^(-1)2/3 , where x<-sqrt(...

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