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Prove that : tan^(-1)(1/5)+tan^(-1)(1/7)...

Prove that : `tan^(-1)(1/5)+tan^(-1)(1/7)+tan^(-1)(1/3)+tan^(-1)(1/8)=pi/4`

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LHS=`tan^(-1)(1/5)+tan^(-1)(1/7)+tan^(-1)(1/3)+tan^(-1)(1/8)`

`tan^(-1) ((1/5+1/7)/(1-1/5xx7))+ tan^(-1) ((1/3+1/8)/(1-1/3xx8))`

`tan^(-1) (6/17)+tan^(-1) (11/23)`

`tan^(-1)((6/17+11/23)/(1-(6xx11)/(17xx23)))`

`tan^(-1)((138+187)/(391-66))`

`tan^(-1)(325/325)`

`tan^(-1) 1=pi/4`
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

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  2. tan^-1 (3/4) + tan^-1 (3/5) + tan^-1 (8/19)

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  3. Prove that : tan^(-1)(1/5)+tan^(-1)(1/7)+tan^(-1)(1/3)+tan^(-1)(1/8)=p...

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  4. Prove that : cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3

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

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  6. If a > b > c >0 , prove that cot^(-1)((a b+1)/(a-b))+cot^(-1)((b c+1)...

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

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

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  9. Solve: tan^(-1)((x-1)/(x+1))+tan^(-1)((2x-1)/(2x+1))=tan^(-1)((23)/(36...

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  10. If a ,\ b ,\ c >0 such that a+b+c=a b c , find the value of tan^(-1)a+...

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  11. Solve the equation: tan^(-1)sqrt(x^2+x)+sin^(-1)sqrt(x^2+x+1)=pi/2

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  12. If a1,\ a2,\ a3,\ ,\ an are in arithmetic progression with common...

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

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

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

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  16. If tan ^(-1 )""(yz )/( xr ) + tan ^(-1 )""(zx)/(yr) + tan ^(-1) "...

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

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

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

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