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Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(...

Prove that: `tan^(-1)(1/2tan2A)+tan^(-1)(cota)+tan^(-1)(cot^3A)={0,ifpi/4 < a < pi/2pi,if0 < A < pi/4`

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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. If a , b , c >0 and s=(a+b+c)/2,p rov et h a t tan^(-1)sqrt((2a s)/(b...

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  2. Simplify [(3sin2alpha)/(5+3cos2alpha)] +tan^(-1)[(tanalpha)/4] ,w h e ...

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  3. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cota)+tan^(-1)(cot^3A)={0,ifpi...

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

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

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  6. Prove: tan^(-1)(1/4)+tan^(-1)(2/9)=sin^(-1)(1/(sqrt(5)))

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  7. Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

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

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  9. Solve for x: tan^-1(x+1)+tan^-1(x-1)=tan^-1(8/31)

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  10. Solve : tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x

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

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  12. Solve for x : cot^(-1)x-cot^(-1)(x+2)=pi/(12) , where x >0

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

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

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

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

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

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

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  19. Prove that : sin^(-1)(8/(17))+sin^(-1)(3/5)=sin^(-1)((77)/(85))=tan^(-...

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  20. Prove that:cos^(-1)((12)/(13))+sin^(-1)(3/5)=sin^(-1)((56)/(65))

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